Human Movement Science 5 (1986) 373-391

North-Holland

373

SIMULATION STUDY OF A DECISION-MAKING MODEL OF SQUASH COMPETITION, PHASE TWO: TESTING THE MODEL THROUGH THE USE OF COMPUTER SIMULATION

Claude SARRAZIN *, Claude ALAIN and Daniel LACOMBE

Unioersq of Montml, Cumda

Sarrazin, C., C. Alain and D. Lacombe, 1986. Simulation study of a decision-making model of squash competition, phase two: testing the model through the use of computer simulation. Human Movement Science 5, 373-391.

This study aims at verifying the inner validity and logic of a squash competition decision-making model through the use of computer simulation. The model defines the cognitive-decisional

strategy of the defending player (D) when selecting a motor reaction in response to his opponent’s

shot. Computer simulation of the model was carried out on a PDP-10 computer using a recent

version of UCI-LISP. Protocol analysis data pertaining to the nature of the information D

processes when awaiting the attacking player’s shot were fed into the simulation program in order

to examine the extent to which the model can reproduce decisions reached in various defensive

contexts. Simulation results reveal that the proposed model can account for a substantial part of

the variation in the speed and accuracy of D’s motor reaction in real sport situations. Several

factors like time pressure, expectancies, uncertainty, recency and familiarity of the relationship

between signal and response appear to affect D’s motor response via the cognitive-decisional

strategy employed by the defending player. Particular discrepancies observed between simulation

results and decisions reached by expert players in specific defensive situations nevertheless

indicate that the decision rule utilized within the present model needs to be refined. In this regard,

several issues are discussed and suggestions for further simulation studies are put fonvard in order

to account more precisely for the various features characterizing the defensive player’s motor

reaction in real sporting context.

An important determinant of sport performance is the speed and accuracy of the response one has to initiate to counter an opponent’s attack. The player which is in a defensive position, may be viewed as confronted to a choice reaction time (CRT) task. A perceived signal will trigger a specific motor reaction in response to one of various possible events.

* Address correspondence to C. Sarrazin, Departement d’kducation physique, Universite de Montreal, C.P. 6128, succursale A, Montrkal, Quebec, H3C 357. Canada.

0167-9457/86/$3.50 0 1986. Elsevier Science Publishers B.V. (North-Holland)

374 C. Sarruzin et al. / Computer simulation: decision-making in sqwsh

Experimental studies conducted in the field of human performance have stressed the importance of several factors affecting reaction speed: the amount of uncertainty calculated in ‘bits’ of information (Hick 1952; Hyman 1953), compatibility between signal and response (Fitts and Seeger 1953), familiarity of the relationship between signal and response (Mowbray and Rhoades 1959; Teichner and Krebs 1974), recency or repetition effect (Kirby 1980), time pressure (Fitts 1966; Garrett 1922; Pachella and Pew 1968), correct prediction of stimuli (Bernstein and Reese 1965; Whitman and Geller, 1972), probability of occurrence of stimuli (see review by Welford (1980)), confidence in the accuracy of stimuli prediction (Geller and Whitman 1973), etc.. .

Although fundamental to the understanding of the human performer, these studies may not be sufficient to account for all the determinants of motor reaction in a sporting context. Indeed, reaction speed as well as the relevance of the motor response may depend, for a large part, on the information processing realized before the occurrence of the reac- tion signal. This processing which is by-passed in CRT experiments, is likely to imply a complex integration of information originating from numerous interacting sources. To this point, however, little is known about the precise nature of this information, how it is actively organized and utilized by the performer and how it might affect the speed and accuracy of the motor reaction.

The study reported hereafter addresses these questions in light of information processing theory and methodology (Newell and Simon 1972; Simon 1979) as applied to decision-making (Payne 1980, 1982). It is part of a more extensive research program aiming at identifying the cognitive information processing strategy underlying decision processes used by the defending player (D) in squash competition. Phase one of this research program has been completed. It consisted of obtaining (Alain et al. 1983) and analyzing (Sarrazin et al. 1983) typical protocols of expert squash players placed in a real game situation. A protocol is a detailed account of all the information a performer has to process in a given situation as well as a precise description of his or her behavior in this same situation. The analysis of the protocol (Sarrazin et al. 1983) has led to the formulation of a conceptually viable model of the information processing strategy and decision-making process of D in squash. Through the use of computer simulation, the aim of the present study is (1) to test the intrinsic validity and logic of this model, and (2) to assess the extent to which it accounts for the influence of some of

C. Surruzin et al. / Computer smulation: decision-makrng rn squash 315

the factors affecting the speed and accuracy of a performer’s motor reaction.

Information processing and decision-making model

The defending player (D) is viewed as an information processing system (IPS: Newell and Simon 1972) having to reach a decision. This decision consists in selecting an appropriate preparatory state for a specific motor response which will be performed upon perception of a reaction signal. This signal corresponds to the ball-racquet contact of the attacking player and the response is D’s motion toward the ball just hit.

A preparatory state is regarded as the particular bias awarded by the player to the chosen response. Results of a preceding investigation (Alain et al. 1983) revealed that expert squash players advocate three different preparatory states: (2) Total Preparation (TP) according to which D totally favors a unique response to be executed without considering any other possible responses. TP is assumed to greatly increase reaction speed but, as a counter part, to enhance the risk of undertaking erroneous actions. (2) Partial Preparation (PP) whereby D primes one response without excluding the possibility that an alternate reaction may be required. Reaction time will be shorter if the primed response is the one appropriate to the opponent’s shot, otherwise reaction outset will be delayed. (3) Equal Preparation (EP) according to which D’s bias is the same for each of the possible responses. EP diminishes the risk of erroneous reactions but further lengthens reac- tion time.

In the literature the concept of preparation is restricted to true reaction time situations. It is viewed as a modification of decision processes taking place before the occurrence of the reaction stimulus and resulting in the reduction of the time needed to complete the necessary information processing operations (e.g., stimulus identifica- tion, response selection, response programming) conducted once the reaction stimulus has been presented (see Holender (1980) for a more detailed discussion). This definition excludes the notions of anticipa- tions and guesses because, in such instances, the information processing operations normally encountered in true reaction time situations after the stimulus has appeared, are simply by-passed. However, in sporting contexts the player is often forced to engage in anticipatory and

376 C. Surrctzrn et al. / Computer smulcrtron: decision-making in syuush

guessing behavior. For this reason, the meaning of the term prepara- tion, as it is used in this paper, encompasses anticipatory and guessing modes of behavior as well as true reactions. More specifically the term preparation will refer to modifications of decision processes taking place before the occurrence of the reaction stimulus and resulting in either the by-passing of the information processing, normally encoun- tered in true reactions, after the stimulus has appeared, or the reduc- tion of time needed to complete these operations when they are undertaken.

Selection of an appropriate preparatory state is the result of a decision-making process involving information processing and the ap- plication of a decision rule before the occurrence of the reaction signal. D’s decision process begins from that moment he, himself, hits the ball (preparatory signal). According to protocol analysis (Alain et al. 1983; Sarrazin et al. 1983), the information D processes may be divided into three categories. The first refers to the class of information used by D to evaluate the subjective probabilities of the different shots (ex- pectancies) that might be executed by his opponent; it encompasses the respective positions of the players on the court, play habits of the attacking player, the opponent’s ability to aim the ball to the chosen spot, the angle of the attacking player relative to the front wall and the player’s motion when driving the ball. The second category pertains to the information relative to time pressure. This factor is derived from a ratio of two estimated time values: the time available to reach the position where the ball is expected to land (TA) and the estimated time required to reach this position (TREQ). The last category of informa- tion comprises several psychological factors that appear to be of obvious importance to the players. These are, inter alia, the stake or significance of the game, the score in the game, the strategy adopted by the player and the tiredness of the two opponents.

The sequential processing of each category of information results in the computation of three distinct functions (Alain et al. 1983): (1) Ps which assigns a subjective probability to each of the possible shots, (2) PO which estimates the chance of returning the ball in play, given a specific time pressure (TA/TREQ ratio), and (3) Uu, a utility function that determines the usefulness of adopting a particular preparation state in view of the influence of psychological factors.

The computed values of the three functions are utilized afterwards to select the best motor reaction, that is the best preparation state for the

C. Surruzin et al. / Computer simulation: decuion-making in squush 311

most appropriate motor response. This last phase of the decision process (application of a decision rule) is assumed to be realized (Alain et al. 1983) according to the subjective expected utility (SEU) principle (see Coombs et al. 1970). Values of the three above functions are used to compute and assign an SEU value to each of the possible motor preparations and D is expected to choose that preparation with the highest SEU value.

D’s decision process does not unfold fortuitously. It is considered to be governed by a predetermined cognitive strategy (Alain et al. 1983). Protocol analysis techniques (Newell and Simon 1972) utilized by Sarrazin et al. (1983) has led to the suggestion that this strategy basically rests on an internal symbolic representation of the task environment and the use of a specific operational algorithm, both stored in some long-term memory (LTM). The internal symbolic repre- sentation is a highly structured inner organization of all past and present information acquired by the player in relation to the task at hand. The algorithm is responsible for processing this information and carrying out the decision process. It consists of a series of sequentially and logically organized actions. An action corresponds either to the establishment of a goal or to the application of an operator. A goal sets the IPS to search for missing information to be processed by an operator. This search is realized within the internal representation of the task environment. An operator is a computational device generating new states of information from old.

Activation of specific algorithms’ actions depends on the current state of information in short-term memory (STM). This current state of information is in turn a function of actions’ outcome as well as of incoming data from external reality. Thus, the cognitive strategy un- derlying D’s decision process essentially consists in sequentially shifting from one knowledge state (structured set of information) to the other until selection of an appropriate motor preparation can be achieved. A detailed description of the above-proposed model can be found in previous papers by Alain et al. (1983) and Sarrazin et al. (1983).

Computer simulation

Simulation program

Simulation of D’s cognitive strategy was realized on a PDP-10 computer using a recent version of UCI-LISP (Meehan 1979) and an

378

Table 1

Production rules P,, P2 and Pg.

Computer trace Cognitive-decisional behavior

P, : Heurtstic = First Pi : Find the first predicate T of an iteration

and evaluate it.

Iteration 1

Predicate = (EQ(Preparation-P)

(Quote Note))

Process = Print solution

Produce = Stop

Iteration 1 = if D has already selected a

motor preparation, print D’s choice and stop

the processing.

Iteration 2

Predicate = T

Process = Nothing

Produce = Pz

Iteration 2 = by default, the predicate is T

and D sets the goal of evaluating the next

production.

Pz : Heuristic = First Pr : Find the first predicate T of an iteration

and evaluate it.

Iteration 1

Predicate = (EQ(Preparation-P) (Quote, Uncertain))

Process = Nothing

Produce = P3

Iteration 1= if D is uncertain of the motor

preparation to choose then D sets the goal of

finding the best possible motor preparation.

P9 : Heuristic = All Ps : Evaluate every iteration that has a predi- cate T.

Iteration 1

Predicate = (EQ(POS-P) (Quote Desire))

Process = (DPOS)

Produce = Stop

Iteration 2

Predicate = (EQ(ORI-P) (Quote Desire))

Process = (DORI)

Produce = Stop

Iterations 1, 2, 3, 4, 5 = the same principle is

governing all of these iterations. If D is

uncertain of the motor reaction to choose

and D wants to change or to give a value to

the expression position (or orientation, shot,

habits, ability) then D applies operator DPOS

(or DORI, ID, DHABITUD, DABILIT) and stop the evaluation of this iteration.

Iteration 3

Predicate = (EQ(ID-P) (Quote Desire))

Process = (ID)

Produce = Stop

Iteration 4

Predicate = (EQ(HABD-P) (Quote Desire))

Process = (DABILIT)

Produce = Stop

Iteration 5

Predicate = (EQ(HABL-P) (Quote Desire)) Process = (DABILIT)

Produce = Stop

C. Sarrazin et al. / Computer simulation: decision-makmg rn squash 379

Table 1 (continued)

Computer trace Cognitive-decisional behavior

Iteration 6 Iteration 6 = D uses the information assessed

Predicate= (OR(EQ(POSP) (Quote Note)) by iterations 1 to 5 to assign subjective

(EQ(ORI-P) (Quote Note)) probabilities to the attacking player’s poten-

(EQ(ID-P) (Quote Note)) tial shots.

(EQ(HABD-P) (Quote Note))

(EQ(HABL-P) (Quote Note)))

Process = (ASPS)

Produce = Stan

adapted translation of Winston’s (1977) production system interpreter. The algorithm governing D’s strategy is operationalized by means of eight production rules (P,, P2, P3, P4, Ps, P,, PI5 and P,,), each encompassing one or more iterations. These production rules provide, within the simulation program, a formal representation of the produc- tion system defined by Sarrazin et al. (1983).

Iterations are programming devices embodying the modus operandi of the algorithm’s actions. They are always composed of a predicate-process-produce triad. ‘Predicates’ are simple functions de- termining whether or not current states of information in STM corre- spond to actions’ execution conditions. If the conditions are met, the ‘predictate’ function value is true (T) and the triad’s process-produce components are carried out.

‘Processes’ consist of using operators for information processing purposes. In fact, operators correspond to computational functions designed to process information. Fourteen operators have been defined using basic LISP functions (Meehan 1979). Among these, operators ASPS, ASPR and ASVU respectively specify the computational logic of the three functions - Z’s, PO and Uu - described in the preceding section. Operators DPOS (determine players’ position), DORI (de- termine opponent’s orientation), ID (identify possible shots), DHABI- TUD (determine opponent’s habits), DABILIT (determine opponent’s ability), PR-TEMP (evaluate time-pressure), DPOINT (determine score), DSTR (determine strategy) and DFAT (determine tirednesss) assess relevant information to be utilized by operators ASPS, ASPR and ASVU. Finally, operators SEU and CHOICE are responsible for computation of the decision rule in accordance with the SEU principle (see preceding section).

380 C. Sarrann et nl. / Computer simulutron: decisron-mukrng rn squash

‘Produces’, the third component of the predicate-process-produce triad, either designates goals or puts a stop to iterations’ assessment. Within the simulation program’s framework, goals essentially point to the next production rule to be used by the system. By doing so, the program sets the system to search for missing information.

Finally, two different heuristics are employed to specify the func- tioning of each production rule. Heuristic FIRST causes a production to localize the first iteration with a true predicate. The iteration’s process is then carried out and the next production rule to be utilized is pointed out. Heuristic ALL brings about the evaluation of all the production’s iterations holding a true predicate. For illustrative pur- poses, three production rules (Pi, P2 and P,) are described in table 1.

Simulation results

Using data obtained from typical protocols of expert squash players (Alain and Sarrazin 1985; Alain et al. 1983; Sarrazin et al. 1983), several simulations of the above described model of D’s decision process were carried out. These data essentially refer to information sources expert players acknowledge taking into consideration in various typical defensive situations. Details concerning the methodology used to obtain and analyze protocols can be found elsewhere (Alain and Sarrazin 1985; Alain et al. 1983; Sarrazin et al. 1983). Protocol analysis data were fed into the simulation program in order to examine the extent to which the model can reproduce decisions reached by different players in various defensive contexts. Table 2 illustrates a representa- tive simulation trace which successfully accounts for a defensive player’s decision behavior. The trace also elucidates and confirms the model’s inner logic.

The simulation program first defines (table 2A) the internal rep- resentation of the task environment within D’s LTM as well as the initial current state of information within D’s STM. In this particular situation, D is aware of his own position and orientation on the court as well as his score, tiredness and strategy at this point of the game (early situation in game). D also knows his opponent’s score. In addition, D has elaborated in LTM some internal representation of (1) his opponent’s habits and ability in relation to different shots, (2) shots’ time pressure, (3) preparation state (PS) efficacy, and (4), energy cost resulting from adoption of a specific PS.

Given this particular initial knowledge state, D’s decision process begins. The process computational phases are given in table 2B. The first column indicates the production rules employed throughout the decision process. Each specific production rule corresponds to a de- termined computational phase. Column 2 gives production rules’ iter- ations which have been evaluated and column 3 refers to iterations’

produces. The simulation trace, which is a result of iterations assessment, is

presented in table 2C. This trace shows that D processes sequentially all relevant information that allow computation of the three basic functions - Ps (ASPS), PO (ASPR) and Uu (ASVU) - of the decisional model. Outputs of operators DPOS, DORI, ID, DHABITUD and DABILIT first provide D with sufficient information to assign a subjective probability (ASPS) to each shot he suspects the opposing player might use (0.357 for a boast-shot and 0.643 for a pass-shot). Considering next the time pressure of each possible shot (PR-TEMP), D estimates his chances of a successful motor reaction. Through the use of operator ASPR, five probabilities of successfully returning the ball into play are associated to each possible shot in relation to the five specific motor preparations (here: TP for a boast, TP for a pass-shot, PP for a boast, PP for a pass-shot and EP) D might select.

The following computational phase brings D to ascribe utility weights (1 or 2) to the different motor reactions in consideration of several information sources such as the game score (DPOINT), his own defensive strategy (DSTR) and his tiredness (DFAT). These utility weights are then combined in order to compute (ASVU) an overall utility weight for each motor preparation.

During the last phase of the decision process, outputs of operators ASPS, ASPR and ASVU are utilized to evaluate the subjective ex- pected utility value (SEU value) of each possible motor reaction. This computation is realized in accordance with the SEU principle. The following equation illustrates the integrative process employed to com- pute the SEU value corresponding to a TP state for the boast shot:

SEU, = (ASPS, * ASPR, + ASPS,, * ASPR,) * ASVU, ,

where b is for ‘boast-shot’ and p is for ‘pass-shot’. Using the values of ASPS, ASPR and ASVU underlined in table 2C, the SEU, index becomes 1.785. Application of the same computational principle to

382 C. Sarrazin Ed 01. / Computer simulution: decision-making in squash

Table 2

Simulation trace of D’s decision process

A. Internal representation of tusk environment

Defensive player

Position

Orientation

Score Tiredness

Strategy Habits

Ability

Time-pressure

PS-efficacy

PS-energy-cost

Attacking player

Score

10

Face 8

Exhausted

Fake

((Boast 0.600) (Lob 0.199) (Drop-shot 0.000) (Pass-shot 0.799))

((Boast weak) (Lob weak) (Drop-shot weak) (Pass-shot strong))

((Boast low) (Lob low) (Drop-shot high) (Pass-shot high))

((TP augmented) (PP augmented) (EP diminished))

((TP normal) (PP normal) (EP exhausting))

2

B. Compututionul phuses

Production rules Iterations Produces

PI

P2

P3 P4

P5

P9

P9

P9

P9

P9

P9

P5 P15

P15

P5

P17

P17

P17

P17

P5

P3 Pl

2 W) 1 (P3) 2 (P4) 1 (P5) 1 (P9) 1 WJP) 2 FOP) 3 FOP) 4 WOP) 5 WP) 6 WOP) 2 (P15) 1 (Stop) 2 WOP) 3 (Pl7) 1 WOP) 2 WOP) 3 WJP) 4 WOP) 4 (P3) 1 (Pl) 1 (Stop)

C. Sarrazin et ul. / Computer simulation: decision-mukirzg in squash

Table 2 (continued)

383

C. Simulation trace of decision process

* (SetQ actionFLG T)

* (SetQ BSTrace-P T)

T

* (EXE-P P,)

Operator

DPOS

Operator

DORI

Operator

ID

Operator DHABITUD

Operator

DABILIT

Operator

ASPS

Operator

PR-TEMP

Operator

ASPR

Operator

DPOINT

Operator

DSTR

Operator

DFAT

Operator

ASVU

Operator

SEU Operator

CHOICE

= (10.6)

= (6. Face)

= (Boast pass-shot)

= ((Boast 0.600) (Pass-shot 0.799))

= ((Baost weak) (Pass-shot strong))

= ((Boast 0.357) (Pass-shot 0.643))

= ((Boast low) (Pass-shot high))

= ((Boast (s 0.799 1.0 0.899 1.0)) (Pass-shot

(0.0 0.899 0.300 0.799 0.300)))

= (2 2 1 1 1)

= (2 2 2 2 2)

=(l 11 11)

=c55444)

= (1.785 4.322 2.200 3.343 2.200)

= SEU value no 2

Total preparation for boast = 1.785

Total preparation for pass-shot = 4.322

Partial preparation for boast = 2.200

Partial preparation for pass-shot = 3.343

Equal preparation = 2.200

Selected motor reaction is

Total preparation for pass-shot = 4.322

each potential motor preparation allows for the determination of the remaining SEU values. Afterwards, availability of these values renders D able to make a decision. He chooses the alternative that has the highest SEU value (operator CHOICE). As indicated in table 2C, the current defensive situation results in the selection of a TP state for the expected pass shot.

Computer simulation further reveals that D’s cognitive-decisional strategy is an important intervening process through which several factors known to affect reaction speed and/or response accuracy may influence motor reactions. For instance, uncertainty, recency or repe- tition effect and familiarity of the relationship between signal and response may affect reaction speed by either increasing or decreasing computational time. As an example, table 3 illustrates the influence of situation repetition (recency effect) on D’s decision process duration. In this particular case, both players did not change position and orientation on two consecutive sequences of a same rally. On the second sequence, D enters the decision process with a better structured initial representation of the defensive situation. In contrast with the internal representation of the task environment shown in table 2A, one can see (table 3A) that pre-established sets of possible shots (P-SHOTS) and utility weights (SCORE-VALUE, STRATEGY-VALUE, TIRED- NESS-VALUE and ASVU-VALUE) are already stored in D’s memory. Given this initial knowledge state, D needs to process less information and uses less computational phases in order to reach a decision (table 3B as compared to table 2B).

Similar results were obtained with respect to the influence of un- certainty. For instance, when D is ignorant of his opponent’s habits, he takes more possible shots into consideration, which, in turn, increases processing time. On the other hand, if D is familiar with his opponent’s habits to such an extent that a particular situation usually results in a determined motor preparation, computational time is greatly reduced. D’s internal representation which is activated upon perception of this situation permits an almost immediate decision through the use of production rule Pi (see table 1).

The influence of the above factors on decision process duration is related to reaction speed in the following way. When computational time is lengthened, reaction signal (ball-racquet contact of the oppo- nent) may occur before D has reached a decision. As a consequence, the decision by default is equivalent to an equal preparation state

Table 3

C. Surrcrzin et al. / Computer simulation: decrslon-muklng in squush 385

Influence of situation repetition on D’s decision process.

A. Internal representation of task environment

Defensive player

Position

Orientation

score

Tiredness

Strategy

Habits

Ability

Time-pressure

PS-efficacy

PS-energy-cost

P-shots

Score-value

Strategy-value

Tiredness-value

ASVU-value

Attacking player

Position

Orientation

Score

B. Compututionul phases

10

Face

8

Exhausted

Fake

((Boast 0.600) (Lob 0.199) (Drop-shot 0.000) (Pass-shot 0.799))

((Boast weak) (Lob weak) (Drop-shot weak) (Pass-shot strong))

((Boast low) (Lob low) (Drop-shot high) (Pass-shot high))

((TP augmented) (PP augmented) (EP diminished))

((TP normal) (PP normal) (EP exhausting))

(Boast lob)

(2 2 1 1 1)

(2 2 2 2 2)

(1 1 1 1 1)

(5 5 4 4 4)

16

Face

5

Production rules Iterations Produces

Pl

P2

P3

P4

P9

P9

PY

P9

P9

P9

P5

P15

P15 P5

P3

Pl

2

1

2

1

1

2

3 4

5

6 2

1

2

4

1

m (P3) (P4)

(P5)

(P9)

WJP)

WP)

WOP) (Stop)

WOP)

(Pl5)

WOP)

WOP)

(P3)

(Pl)

(Stop)

which is expected to yield longer reaction times (Alain and Sarrazin 1985; Alain et al. 1983). Conversely, shorter computational times permit the selection of total or partial preparation states before the

386 C. Sarruzin et 01. / Computer sinmlutron: decisron-mcrkrng in squash

reaction signal occurrence. These preparation states are considered to favor faster reaction times (Alain and Sarrazin 1985; Alain et al. 1983).

Finally, further analysis of the model’s functioning indicates that the type of decision rule D utilizes may be responsible for the influence of expectancies and time pressure on reaction speed and/or response accuracy. For instance, when two equally high time pressure shots are assigned equal subjective probabilities (e.g., 0.5 for a pass shot and 0.5 for a drop shot), the SEU rule favors the selection of a Total Prepara- tion state. However, as observed from a typical expert player’s traces, the SEU values associated with the Total Preparation for each of the two shots are identical, necessitating a random selection of the specific motor response. Thus according to the model, time-pressure may increase reaction speed but may also cause more incorrect reactions due to random selection of the response. In contrast, unequal probabil- ities attributed to the same two shots (e.g., 0.8 for a pass shot and 0.2 for a drop shop) bring about an unequivocal decision in favor of the shot which has the highest subjective probability. On the other hand, two low time pressure shots with equal probabilities generally result in the selection of an Equal Preparation state whereas low time pressure combined to unequal probabilities yields a Partial Preparation state.

However, the above results must be considered cautiously. When possible shots differ in terms of time pressure, decisions obtained from the model often diverge from those reached by expert players. These discrepancies indicate that either the SEU principle may not be totally relevant to the type of decision-making process under study or that players may utilize distinct decision rules in different situations. Another possible explanation is that SEU values may not always be computed from adequate ASPS, ASPR and/or ASVU values. In other words, information processing which precedes application of the SEU princi- ple, may not be comprehensive enough to account for all the subtlety of D’s decision process.

Discussion

The present paper aims at determining the intrinsic validity and applicability of a decision-making model as applied to the field of human performance. Previous studies (Alain and Sarrazin 1985; Alain et al. 1983; 1986) conducted in a squash sporting context have led to

C. Sarrurin et 01. / Computer simulation: decision-making in squush 387

the formulation of a theoretical model of the information processing strategy that may govern the defensive player’s (D) decisional process (Sarrazin et al. 1983). This strategy essentially corresponds to an effective procedure for the performance of a given cognitive task. As pointed out by Longuet-Higgins (1981) the next step after defining an effective procedure is to check if it is logical and really effective by translating it into a programming language and running the program on a computer.

Within the present study, a production rule system provides the programming scheme to translate the cognitive procedure into a pro- gramming language. Production rule systems are problem-solving methods that reproduce human behavior rationally related to an end (Newell and Simon 1972). Within the framework of the decisional model herein proposed, D is viewed as a problem solver having to reach a decision. Thus, a production system is a suitable representa- tional format to implement the logic of the sequential processing underlying D’s decisional procedure. However, it is not herein assumed that human reasoning goes exclusively in terms of production rule systems. Furthermore, given that the simulation program reproduces adequately D’s decisional task, it is not postulated either that human cognitive processes correspond exactly to the program software and its underlying computer hardware.

Computer programs are precise descriptions of behavior, which specify in logical terms some of the psychological procedures that may govern human thinking (Cohen and Feigenbaum 1982). As such, they provide a way of incorporating, or developing as needed, psychological models and theories of human cognition (Longuet-Higgins 1981; Min- sky 1968). This approach to psychological research is termed informa- tion processing psychology (Newell and Simon 1972) and, more re- cently, cognitive science by its practitioners (Cohen and Feigenbaum 1982).

By testing the adequacy of a cognitive-decisional model through the use of computer simulation, the present study is closer to cognitive science than it is to artificial intelligence and expert system building. The purpose of this research is not to arrive at a robot as the perfect squash defender. It rather constitutes an attempt to better understand the phenomenon of decision-making and its possible influence on the speed and accuracy of the performer’s motor reaction. Given that the model is shown to be plausible and logical, the next step is to point out

388 C. Surrcrzin et al. / Computer simdotion: decrsion-making in squash

new directions of research that are suggestive of new experiments or empirical observations. In this respect, computer simulation is also a useful tool as will be discussed hereafter.

With regard to the intrinsic validity of the model, simulation results indicate that the proposed decisional strategy is a logical and viable description of decision-making in a squash defensive setting. Basically, the model assumes that the decision process is governed by a prede- termined cognitive strategy. This strategy consists of a specific al- gorithm (the production rules) stored in the subject’s LTM and activated by STM’s current states of knowledge. As contended by Newell (1980) LTM and STM respectively correspond to a production memory and a working memory.

The cognitive strategy is believed to process information in two successive stages, as suggested by several authors (Kahneman and Tversky 1979; Payne 1976; Payne et al. 1978; Wallsten 1980). The first is an assessment stage which consists of elaborating an internal repre- sentation of the current defensive situation. This representation is a highly structured inner organization of past and present information which permits computation of the three previously defined functions of the model: Ps (operator ASPS), PO (operator ASPR) and Uv (operator ASVU). The second stage pertains to the selection of an appropriate motor preparation through the use of a specific decision rule. This rule which is assumed to operate according to the SEU principle, takes into account all information processing results obtained during the first assessment stage.

The cognitive-decisional strategy herein proposed further appears to be an important intervening process through which several factors may affect reaction speed and/or response accuracy. Simulation results reveal that decision process duration may be influenced by uncertainty, recency and familiarity of the relationship between signal and response whereas the decision rule is particularly sensitive to time pressure and expectancies. Since motor response specific bias (preparation state) depends on decision process duration and on the decision rule, the decision model defined by Alain et al. (1983) and Sarrazin et al. (1983) appears to be a valuable hypothesis for explaining some of the varia- tion in the speed and accuracy of the performer’s behavior in real sport situations.

However, the discrepancies observed between the actual decisions reached by expert players and those predicted. by the simulation

C. Surrurin et nl. / Computer srmulufion: decision-making m squash 389

program indicate that the model needs to be further refined. First, the assessment stage of the cognitive strategy has to be defined more accurately. Simulation results have revealed that information processing carried out during this initial stage of the decision process may some- times cause the decision rule to select an inadequate motor preparation on the basis of misleading values. Further studies are needed in order to better specify, through the use of protocol analysis, how expert players pre-process information before reaching a decision. These stud- ies should permit a more exhaustive identification of the information sources these players take into consideration as well as a more accurate definition of the assessment stage computational logic (better specifica- tion of production rules as well as of operators’ functional logistics).

Second, the model’s functioning analysis has pointed out that even when ASPS, ASPR and ASVU values appear to be adequate, decisions obtained from the model may differ from those reached by expert players, in some particular defensive situations. As suggested previ- ously, this may indicate that the SEU principle is not the most relevant and/or unique decision rule employed when it comes to motor reaction selection. The combination procedure underlying the SEU principle is based on addition and multiplication operations. However, other com- bination procedures have been suggested within different decision-mak- ing models (see Einhorn 1970). Furthermore, Tversky (1972) has pro- posed a theory (elimination by aspects) where no combination process is required.

Application of the SEU principle also implies that the subject will utilize a maximization procedure in order to select the alternative (motor preparation) with the highest SEU value. The use of such a selection procedure necessitates multiple comparisons which may some- times exceed human operator-limited capacity as contended by Holl- nagel (1977) and Slavic (1982). In fact, the computational logic of operators SEU and CHOICE is much more complex than the program- ming logic of any of the operators utilized in the first assessment stage of the decision process. Moreover, during the selection stage of the decision process, much more information has to be maintained in working memory (STM) in order for the computation to be carried out. Thus, the SEU principle may be too demanding with regard to system capacities. The use of other decision rules and/or selection procedures must be examined more closely.

Finally, the model also needs to be refined with respect to what can

390 C. Sarrurin et ul. / Computer .simulation: dectsron-making rn squash

be termed the ‘continuity’ characteristic of the phenomena under consideration. For instance, reaction time has been shown to be a linear function of the amount of uncertainty calculated in bits of information (Hick 1952; Hyman 1953). The slope of this relation also appears to depend on the compatibility between signal and response (Fitts and Seeger 1953) as well as on the familiarity of the relationship between signal and response (Mowbray and Rhoades 1959; Teichner and Krebs 1974). Within the framework of the present model, the concurrent influence of these factors on the computational logic of the decision rule is not entirely explained. In this regard, the model classifies motor preparations (specific preparation state in favor of a particular motor response) into three discrete categories of reaction speed (Total, Partial and Equal preparation state) such that it is difficult to fully reproduce the ‘continuity’ of the relationship between these factors and reaction time. Thus, further refinements of the model should provide a more precise operational definition of motor prepara- tions in relation to reaction time as well as a decision rule that can account for influences other than time pressure and expectancies. In the line of our general research program, we are now conducting several laboratory and field studies relating to the issues raised above.

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