Get Decompositions And Potentials For Normal Form Games - Ssc Wisc

The most common representation of a simultaneous game is normal form (matrix form). For a 2 player game; one player selects a row and the other player selects a column at the exact same time.

A strategic or normal form game is a particular type of model of interacting decision-makers. In recognition of the interaction, we refer to the decision-makers as players. Each player has a set of possible actions.

In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent the game by way of a matrix.

A normal form game Γ is a three-tuple [N,(Si)i∈N ,(ui)i∈N ] where N is the set of players, Si is player i's strategy set, and ui : ∏i∈N Si → R is player i's payoff or utility function.

1. The extensive-form representation, in which the above information is explicitly described using game trees and information sets; 2. The normal-form (or strategic-form) representation, in which the above informa- tion is summarized by use of strategies.

List of games GamePlayersStrategies per playerCoordination gameNvariableCournot game2infiniteDeadlock22Dictator game2infinite34 more rows

We show that any normal form game can be uniquely decomposed into either (i) a zero-sum equivalent game and a normalized common interest game, or (ii) a zero-sum equivalent potential game, a normalized zero-sum game, and a normalized common interest game, each with distinctive equilibrium properties.