Zero Sum Games As Distributed Cognitive Systems

In the case of two individuals in a competitive situation, or “game,” the game itself (i.e. the players, the rules, the equipment) can be considered to constitute a distributed cognitive system. However, the dominant model of competitive behavior is game theory (VonNeumann & Morgenstern, 1944), which has traditionally treated individuals as isolated units of cognition. By simulating game playing with neural networks, and also by using human subjects, it is demonstrated that the interaction between two players can give rise to emergent properties which are not inherent in the individual players. Recent work in distributed cognition (e.g. Hutchins, 1994; Norman, 1993; Zhang, 1997; Zhang & Norman, 1994) has indicated that cognitive processing can take place across distributed systems composed of multiple, interacting cognitive systems. For example, navigating a large ship, such as a naval vessel, is accomplished through interactions amongst specially trained humans and specialized equipment (Hutchins, 1994). Distributive systems involving more than one agent are prototypically cooperative in nature, in that the agents involved benefit from the function of the distributed system (e.g. a ship avoids sinking). However, distributed systems may also result in situations in which some individuals benefit at a cost to others. The simplest example of this is the case of two individuals in a zero sum game (i.e. a game in which only one player can win). Games such as this can be thought of as distributed cognitive systems with the goal of choosing one player as the winner. Although game playing clearly involves interactions between the players, it does not necessarily follow that we need to consider the distributed properties of a game in order to understand the behavior of a player. This depends on whether the functionality of the cognitive mechanism used by an individual player can be understood in isolation, or needs to be interpreted in terms of the role it plays in the distributed system. The answer to this question will depend to some degree on our assumptions concerning the game playing process. For example, game theory (VonNeumann & Morgenstern, 1944) describes how rational players should behave in a competitive situation prescribed by rules and with payoffs for certain results. However, in order to do this it is necessary to make assumptions concerning the cognitive mechanisms available to the players. One assumption that is frequently made is that players have the ability to generate random responses (i.e. to draw responses at random from a predetermined distribution). For example, the game theory solution for Paper, Rocks and Scissors (hence forth PRS) is to play randomly, 1/3 paper, 1/3 rocks, and 1/3 scissors (in PRS play: paper beats rocks, rocks beats scissors, and scissors beats paper). With this assumption in place there is nothing to be gained by viewing PRS as a distributed system because players' interactions are limited to tossing out and receiving random responses. However, the assumption of random responses is problematic for two reasons. The first is that people are normally quite bad at generating random responses (see Tune, 1964, and Wagenaar, 1972 for reviews), and the second is that when people guess what is coming next in a series they attempt to capitalize on sequential dependencies, regardless if they are present or not (e.g., Anderson, 1960; Estes, 1972; Restle, 1966; Rose & Vitz, 1966; Vitz & Todd, 1967; Ward, 1973; Ward & Li, 1988). Given the above research, a more realistic model of PRS play would have players trying to detect each others sequential dependencies. Note that the story is now different if we consider the players in isolation or if we consider them within the context of the distributed system formed by the game. Taken in isolation, a player's strategy appears passive, limited to searching for sequential dependencies in their opponents responses. However, from the distributed perspective the situation is highly interactive as each player both drives, and is driven by, their opponent's responses (i.e. my behavior would be based on my beliefs about sequential dependencies in my opponents play, which would be driven by my opponents behavior, which in turn is driven by my behavior in a similar way) . The question is, whether this highly interactive situation can impart an alternative functional significance to a sequential detection mechanism?