In the paper “Comments on the Interpretations of Game Theory,” published in Volume 59, Issue 4 of
Econometrica in July 1991, Ariel Rubinstein discusses notions of game theory and strategy that aims to highlight some of the inconsistency between the interpretation and application. Rubinstein argues that equilibrium strategy describes not only a player’s plan of action, but also the considerations that support the optimality of the plans. The paper also argues that models should encompass the perception of a real life situation by the decision makers. Game theory, as Rubinstein writes, is not simply about abstract mathematics but about the real world.
The first half of the paper deals with the notion of strategy. Rubinstein argues that the conventional interpretation is inconsistent with the way it is applied, leading to confusion. In one of the contexts, Rubinstein talks about extensive games with more than one moves. In the game, a player’s strategy is required to specify an action for each node in the game tree corresponding to that player’s movement. However, the incongruence comes when an action must be specified, even after earlier moves that would make the subsequent decision point inconsistent with the earlier moves. The necessity of this specification stems from the need to determine subgame-perfect equilibrium to test the rationality of the plans. In all, a strategy needs to encompass not only the player’s plan, but also the opponents’ belief in the chance that the plan was not followed.
Rubinstein also looks at the interpretation of strategy in mixed strategies. While intuitively problematic, there are clear cases in which players choose random actions, preferring over pure strategies. One interpretation of mixed strategy is to use a large population and having each occurrence take a random draw of the items from the population. Another interpretation is the purification idea, whereby a mixed strategy is dependent on private information not specified in the model. This interpretation argues that ostensibly random behaviors are actually deterministic. Finally, Rubinstein looks at the case of limited memory, which helps to keep modes of behavior simple. When probabilistic nature of doubt is introduced, there may be additional decision points that are unreachable, but added to the game form merely to allow the discussion of reasoning in the state of doubt.
From these discussions, Rubinstein tries to adopt the view that a game is not “a rigid description of the physical rules of the world,” but instead a “comprehensive description of the relevant factors involved in a specific situation as perceived by the players.” Towards that idea, model should include only the factors perceived by the players to be relevant, making the application of game theory “more of an art than a mechanical algorithm.” Finally, Rubinstein talks about regularity, which is necessary for employing game theory as a descriptive science. Game theory, in conclusion, builds models from intuition and from mathematical knowledge uses deductive arguments, which can’t discover the truth alone. Instead, game theory also deals with psychological elements, which help to distinguish humans from machines, which Rubinstein believes is “more exciting and certainly more meaningful.”
