Recently, the list of solved two-person zero-sum games with perfect information has increased. The state of current knowledge is that many games are a win for the ®rst player, some games are draws, and only a few games are a win for the second player. For games with three outcomes (won, drawn, lost) a game is commonly de®ned as fair if the theoretical value of the game is drawn. For these games...

We examine a solution concept, called the “value,” for n-person strategic games. In applications, the value provides an a-priori assessment of the monetary worth of a player’s position in a strategic game, comprising not only the player’s contribution to the total payoff but also the player’s ability to inflict losses on other players. A salient feature is that the value takes account of the co...

The Nash equilibria of a two person non zero sum game are the solutions of a certain linear complementarity problem LCP In order to use this for solving a game in extensive form it is rst necessary to convert the game to a strategic description such as the normal form The classical normal form however is often exponentially large in the size of the game tree In this paper we suggest an alternat...

The semigroup game is a two-person zero-sum game defined on a semigroup (S, ·) as follows: Players 1 and 2 choose elements x ∈ S and y ∈ S, respectively, and player 1 receives a payoff f(xy) defined by a function f : S → [−1, 1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, ...

A non-zero-sum 3-person coalition game is presented , to study the evolution of complexity and diversity in cooperation, where the population dynamics of players with strategies is given according to their scores in the iterated game and mutations. Two types of dierentiations emerge initially ; biased one to classes and temporal one to change their roles for coalition. Rules to change the hands...

A two-person zero-sum game invented by Andrew Gleason in the early 1950’s has a very simple description and yet turns out to be quite difficult to solve. This game is a stochastic game with an information lag for both players. No strategy with a bounded memory of past moves can be optimal. Yet using the notion of generalized subgames, we show that there exist optimal strategies of a simple natu...

In this paper, we discuss some matrix techniques in game theory. In particular, we give a short proof of the fact that equilibrium pairs of a two-person general-sum game can be found by solving certain systems of linear inequalities, and hence some standard linear programming packages such as LINDO or Maple can be used to do the computation. The technique is also used to study evolutionary game...

We examine the case of a two-person repeated game played by a boundedly rational player versus an unboundedly rational opponent. The former is restricted to strategies which are implementable by connected finite automata. It is shown that the “rational” player has a dominant strategy, and that in some cases the “weaker“ (boundedly rational) player may exploit this fact to “blackmail” him. It is...