W present a diagrammatic method that allows the determination of all Nash equilibria of 2×M nonzero sum games, extending thus the well known diagrammatic techniques for 2 × M zero sum and 2 × 2 nonzero sum games. We show its appropriateness for teaching purposes by analyzing modified versions of the prisoners’ dilemma, the battle of the sexes, as well as of the zero sum game of matching pennies...

When searching game trees, Algorithm SSS* examines fewer terminal nodes than the alphabiata procedure, but has the disadvantage that the storage space required by it is much greater. ITERSSS* is a modified version of SSS* that does not suffer from this limitation. The memory M that is available for use by the OPEN list can be fed as a parameter to ITERSSS* at run time. For successful operation ...

The celebrated minimax theorem for zero-sum games, first discovered by John von Neumann in the 1920s [14, 10], is certainly a foundational result in the theory of games. It states that two players, playing a game with zero-sum payoffs, each have an optimal randomized strategy that can be played obliviously – that is, even announcing their strategy in advance to an optimal opponent would not dam...

Let Xl, X 2 , " . , X n , ... be mutually independent random variables with a common cdf F, which is unknown but belongs to some class F of cdf's. The class F = F(J1., (;2, M) is the set of all cdf's whose mean, variance and domain are -00 < J1. < 00,0 < (;2 < 00, and [Jt M, Jt + M) respectively. It is assumed that they are known. Under an observation cost c,O < C < 00, we consider a stopping p...

We study the computational complexity of solving the following problem: Given a game G played on a finite directed graph G, output all nodes in G from which a specific player wins the game G. We provide algorithms for solving the above problem when the games have Büchi and parity winning conditions and the graph G is a tree with back-edges. The running time of the algorithm for Büchi games is O...

The setup is similar to that of a Bayesian game. The ingredients are: 1. denote a typical type of player i. (q (m) , t (m)). All of these are to be chosen by the mechanism designer. We call the pair Γ = (M, φ) a mechanism. We will consider dominant strategy equilibria in these Bayesian games as well as Bayesian Nash equilibria. Whichever solution concept we adopt, we call φ (m) = (q (m) , t (m)...

A two person (or bimatrix) game is a pair of m x n matrices A. B, with integer entries. This game is played between two players A and B. Player A chooses a row t. player B simultaneously chooses a column j. As a result. A receives a,, (dollars, say), and B receives b,,. An easy way to simplify a bimatrix game is to eliminate from both A and B any strategy (row or column) that is dominated by an...

We study strong stability of Nash equilibria in load balancing games of m (m ≥ 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the workload of the server it chooses. A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is...

In this paper we consider the influence of link restrictions on the price of anarchy for several social cost functions in the following model of selfish routing. Each of n players in a network game seeks to send a message with a certain length by choosing one of m parallel links. Each player is restricted to transmit over a certain subset of links and desires to minimize his own transmission-ti...

&nbsp;The Design and Trial of an Educational Game Based on a Fifth Grade Course Y. MahdaviNasab H. Fardaanesh, Ph.D. E. Talaa&rsquo;ee, Ph.D. J. Haatami, Ph.D. Games as enjoyable activities are of special interest to children, and their use as instructional tools can lead to better learning. In order to design and develop such a game from a constructivist perspective, one of ...