There are two complementary approaches to playing sums of combinatorial games. They can be characterized as local analysis and global search. Algorithms from combinatorial game theory such as Hotstrat and Thermostrat [2] exploit summary information about each subgame such as its temperature or its thermograph. These algorithms can achieve good play, with a bounded error. Their runtime depends m...

In traditional game theory, players are typically endowed with exogenously given knowledge of the structure of the game—either full omniscient knowledge or partial but fixed information. In real life, however, people are often unaware of the utility of taking a particular action until they perform research into its consequences. In this paper, we introduce Socratic game theory to model this phe...

In the Ultimatum Game, two players are offered a chance to win a certain sum of money. All they must do is divide it. The proposer suggests how to split the sum. The responder can accept or reject the deal. If the deal is rejected, neither player gets anything. The rational solution, suggested by game theory, is for the proposer to offer the smallest possible share and for the responder to acce...

In this paper we present a new algorithm for negotiations in non-zero-sum games. Although games have been studied extensively, most game playing algorithms have been developed under the assumption that players do not communicate. Many real-world problems, however, can be modeled as non-zero-sum games in which players may mutually benefit if they coordinate their actions, which requires negotiat...

This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustr...