Abstract
Lower one- or two-dimensional coordination, or potential games, are popularly used to model interactive behavior, such as innovation diffusion and cultural evolution. Typically, this involves determining the “better” of competing solutions. However, examples have demonstrated that different measures of a “good” choice can lead to conflicting conclusions; a fact that reflects the history of game theory in equilibrium selection. This behavior is totally explained while extending the analysis to the full seven-dimensional class of potential games, which includes coordination games.
Highlights
When Schelling (1960) wrote Strategy of Conflict, it pivoted attention from zero-sum games to the more general behavior allowed by games with mutually beneficial outcomes [1]
In [JS2], the [JS1] decomposition is extended to handle more player and strategies.2. One objective of this current paper is to develop a coordinate system that is more convenient to use with a wide variety of choices that include potential games
Questions regarding the various measures for game theory have proved to be difficult to analyze
Summary
When Schelling (1960) wrote Strategy of Conflict, it pivoted attention from zero-sum games to the more general behavior allowed by games with mutually beneficial outcomes (which was appropriate during this Cold War period) [1]. By being a change of basis of the original decomposition, this system still highlights the unexpected facts that Nash equilibria and similar solution concepts (e.g., solution notions based on “best response” such as standard Quantal Response Equilibria) ignore nontrivial aspects of a game’s payoff structure; see [11]. This is the precise feature that answers certain concerns in the innovation diffusion literature. After identifying the source of all conflict with symmetric potential games, the full seven-dimensional class is described
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