n-PLAYER STOCHASTIC GAMES WITH ADDITIVE TRANSITIONS

Abstract: An n-player stochastic game can be seen as a finite collection of n-dimensional matrix games that are being played, one at a time, in an infinite sequence of discrete stages. At each stage the players, who are assumed to have complete information and perfect recall, independently choose their actions. This joint action determines a payoff to each of the players, as well as a transition probability vector according to which the next matrix game will be selected. Here we assume the transitions to be additive (AT), i.e.

COMPLEXITY AND EFFECTIVE PREDICTION (JOINT WORK WITH JOEL SPENCER)

Abstract: Let G = (I,J,g) be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which player 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per stage payoff when the two automata face off. We are interested in the cases in which player 1 is "smart" in the sense that k is large but player 2 is "much smarter" in the sense that m>>k. Let S(g) be the value of G were the second player is clairvoyant, i.e., would know the player 1's move in advance.

STRATEGIC ASPECTS OF TERRORISM (Joint work with Professor Eva Carceles Poveda)

Abstract: We study a strategic game between a terror organization and a number ofcountries. The countries can differ in the political or economic power, theeffectiveness in fighting the terrorist in its base and the effectiveness inprotecting their soil against terror attacks. In addition, they can differin their vulnerability to terror attacks and the damage it causes as well asin the benefit they obtain from cooperating with each other in the waragainst terror. We first study a static two stage game analytically.

ALL-PAY CONTESTS

Abstract:  The paper studies a new class of games, "All-Pay Contests", which capture general asymmetries and sunk investments inherent in scenarios such as lobbying, competition for market power, labor-market tournaments, and R&D races. Players have continuous, non-decreasing cost functions and compete for one of several identical prizes. This allows for differing production technologies, costs of capital, and prior investments, among others.

Discrete Colonel Blotto And General Lotto Games

Abstract: A class of integer-valued allocation games -- "General Lotto games" -- is introduced and solved. The results are then applied to analyze the classical discrete "Colonel Blotto games"; in particular,optimal strategies are obtained for all symmetric Colonel Blotto games.http://www.ma.huji.ac.il/hart/abs/blotto.html

Structural Robustness of Large Games

 ABSTRACTThis short survey (forthcoming in the new Palgrave Dictionary of economics)discusses recent findings on the robustness of Nash equilibria of strategicgames with many semi anonymous players.  It describes the notion ofstructural robustness and its general consequences , as well as implicationsto particular games such as ones played on the web and market games. 

EVOLUTIONARILY STABLE STRATEGIESOF RANDOM GAMES, AND THE VERTICES OF RANDOM POLYGONS (JOINT WORK WITH YOSEF RINOTT)

Abstract: An evolutionarily stable strategy (ESS), a concept introduced by Maynard-Smith and Price (1973), is a strategy that is immune to invasions by rare alternative ("mutant") strategies. Does an ESS always exist? No: there are finite games with no ESS (unlike Nash equilibria, which always exist in this case). How robust is this non-existence phenomenon? In particular, does an ESS exist for almost every game?Next, consider the convex hull of n random points in the plane. How many vertices are there?

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