A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows and n columns). Preferences over acts are complete, transitive, continuous, monotonic and certainty-independent (Gilboa and Schmeidler (1989», an...

In this paper, a gentle introduction to Game Theory is presented in the form of basicconcepts and examples. Minimax and Nash's theorem are introduced as the formalde nitions for optimal strategies and equilibria in zero-sum and nonzero-sum games.Several elements of cooperative gaming, coalitions, voting ensembles, voting power andcollective e ciency are described in brief. Analy...

In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash’s theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and nonzero-sum games. Several elements of cooperative gaming, coalitions, voting ensembles, voting power and collective efficiency are described in brief. Analytical (ma...

The infinite horizon risk-sensitive discounted-cost and ergodic-cost nonzero-sum stochastic games for controlled Markov chains with countably many states are analyzed. For the discounted-cost game, we prove the existence of Nash equilibrium strategies in the class of Markov strategies under fairly general conditions. Under an additional geometric ergodicity condition and a small cost criterion,...

(mh-query 1000 100 ;Monte Carlo Inference ;CONCEPTS (define personstrength (mem (lambda (person) (gaussian 10 3)))) (define lazy (mem (lambda (person game) (flip 0.1)))) (define (teamstrength team game) (sum (map (lambda (person) (if (lazy person game) (/ (personstrength person) 2) (personstrength person))) team))) (define (winner team1 team2 game) (if (< (teamstrength team1 game) (teamstrength...

Lines of Action (LOA) is a two-person zero-sum game with perfect information; it is a chess-like game with a connection-based goal. In this note the 6 × 6 variant of LOA is weakly solved. A Proof-Number search method, PN, is used to compute that the game is a win for the first player (Black). Based on the results of solving the boards up to 6× 6, an optimistic time frame is given for solving 7×...

In this section we study games with only two players. We also restrict attention to the case where the interests of the players are completely antagonistic: at the end of the game, one player gains some amount, while the other loses the same amount. These games are called “two person zero sum games”. While in most economics situations the interests of the players are neither in strong conflict ...