It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence a...

We introduce a two-person beauty contest game with a unique Nash equilibrium that is identical to the game with many players. However, iterative reasoning is unnecessary in the two-person game as choosing zero is a weakly dominant strategy. Despite this “easier” solution concept, we find that a large majority of players do not choose zero. This is the case even with a sophisticated subject pool...

Under the notable Issacs’s condition on the Hamiltonian, the existence results of a saddle point are obtained for the stochastic recursive zero-sum differential game and mixed differential game problem, that is, the agents can also decide the optimal stopping time. Themain tools are backward stochastic differential equations BSDEs and double-barrier reflected BSDEs. As the motivation and applic...

The set Gn of all n-person games 1 may be considered a convex subset of a euclidean space; Gn has dimension 2 n — n — 2. Although it has not been proved that all games possess a solution, large classes of solvable games have been discovered. In [2], Shapley defined a certain class of solvable games—the quota games—and showed that from the point of view of dimension, the set Qn of all ^-person q...

We have seen that Nash equilibria in two-player zero-sum games (and generalizations thereof) are polynomial-time tractable from a centralized computation perspective. We have also seen that the payoff matrix of a zero-sum game determines a unique value for the row player and a unique value for the column player (summing to zero), which specify their payoffs in all equilibria of the game. In thi...

Multistage robust optimization problems can be interpreted as two-person zero-sum games between two players. We exploit this game-like nature and utilize a game tree search in order to solve quantified integer programs (QIPs). In algorithmic environment relaxations are repeatedly called asses the quality of branching variable for generation bounds. A useful relaxation, however, must well balanc...

The paper is concerned with two-person zero-sum mean-field linear-quadratic stochastic differential games over finite horizons. By a Hilbert space method, necessary condition and sufficient are derived for the existence of an open-loop saddle point. It shown that under condition, associated two Riccati equations admit unique strongly regular solutions, in terms which point can be represented as...

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, ...

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to nd the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a...