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Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles
Author(s) -
Ma Wenjun,
Luo Xudong,
Jiang Yuncheng
Publication year - 2018
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21950
Subject(s) - nash equilibrium , mathematical economics , best response , normal form game , lottery , epsilon equilibrium , stochastic game , strategy , correlated equilibrium , symmetric game , interval (graph theory) , risk dominance , equilibrium selection , complete information , solution concept , computer science , bayesian game , traveler's dilemma , repeated game , game theory , mathematics , combinatorics , statistics
In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.