Theory of Moves
Modeling social situations is complicated. In order to effectively analyze strategic behaviors of people, game theory often involves representing players’ strategies with models. Classic models include the payoff matrix, the “normal form”, or the game tree, the “extensive form” (562). In his paper, “Theory of Moves”, SJ Brahms presents a new way to model games that adds “a dynamic dimension” (562) to classical game theory.
Theory of Moves incorporates a temporal aspect in its model. It allows players to look into the past and the future to evaluate possible moves and opponents’ moves and countermoves. This type of thinking leads to different equilibria than classical game theory analysis.
Players can rank possible outcomes from best to worst, but this ordering does not indicate degree of preference. The model also allows for power differences among players as it allows for players to interact with each other beyond simply making moves; one player could, for example, “carry out threats when necessary” (563). Lastly, the model does not assume all players share the same information, allowing for misperception and deception.
The theory has six basic rules:
- A game starts at an “initial state”, a row and column intersection of a payoff matrix.
- Either player can switch strategies, changing the outcome, and Player 1 moves first.
- Player 2 can move (after Player 1 moves).
- Players alternate responding until neither switches strategies. This resulting outcome is the “final state” which is the only point at which players reap payoffs and marks the end of the game.
- A player only moves when it leads to a preferred outcome based on his anticipation of the final state.
- Two-player evaluates the calculations of the other players before moving, considering their possible moves, other players’ possible counter moves, and corresponding counter moves, continually.
To illustrate the theory of moves more clearly, I will illustrate with the Prisoners’ Dilemma.
Above is the model of theory of moves for the Prisoners’ Dilemma. Each suspect has 2 strategies: confess and remain silent. The numbers in the matrix reflect the payoffs for each suspect in each outcome with 4 being the best payoff and 1 the worst. If the dilemma begins at (confess, confess), neither suspect would want to move so (confess, confess) is an equilibrium. If the dilemma begins at (silent, silent), each suspect can look ahead and see that switching their strategy to confess would cause the other suspect to also switch their strategy to confess, producing the (confess, confess) equilibrium. As each suspect is better off in the (silent, silent) outcome, both suspects will decide to not move, making (silent, silent) an equilibrium. Lastly, if the dilemma begins with one suspect confessing and the other remaining silent, the confessing suspect, knowing that the silent suspect would change his strategy to confess, producing the (confess, confess) equilibrium, will change his strategy to compromise in order to produce the (silent, silent) equilibrium which is better for him than (confess, confess).
In classical game theory, both suspects have a dominant strategy to confess and has only one equilibrium at (confess, confess). Theory of moves, on the other hand, produces equilibria at (confess, confess) and (silent, silent) by combining a game tree and a payoff matrix to view the situation with more dimension.
Theory of moves seems to provide more insight into situations. The added dimensions of time, initial states, and continual strategy evaluation and adjustment allow for a perspective on games different from what classical game theory provides, and may be in some cases a more accurate analytical model.
Works Cited