Economists use the word rational in a narrow way. To an economist, a rational actor is someone who makes decisions that maximize her (or his) preferences subject to constraints imposed by the environment. So, this actor knows her preferences and knows how to go about optimizing. It is a powerful approach, but it probably is only distantly related to what you mean when you think of yourself as r...

We consider dynamic electromagnetic evasion-interrogation games where the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies to enhance detection. The resulting problem is formulated as a two-player zero-sum dynamic differential game in which the cost functional is based on the expected value of the in...

Original scientific paper A zero-sum game approach for H∞ robust control of continuous-time singularly perturbed bilinear quadratic systems with an additive disturbance input is presented. By regarding the stochastic disturbance (or the uncertainty) as "the nature player", the H∞ robust control problem is transformed into a twoperson zero-sum dynamic game model. By utilizing the singular pertur...

We consider a large community of individuals who mix strongly and meet in pairs to bet on a coin toss. We investigate the asset distribution of the players involved in this zero-sum repeated game. Our main result is that the asset distribution converges to the exponential distribution, irrespective of the size of the bet, as long as players can never go bankrupt. Analytical results suggests tha...

Given a two-player zero-sum discounted-payoff stochastic game, we introduce three classes of continuous-time best-response dynamics, stopping-time best-response dynamics, closed-loop best-response dynamics, and open-loop best-response dynamics. We show the global convergence of the first two classes to the set of minimax strategy profiles, and the convergence of the last class when the players ...

A zero-sum perfect information game is one where every player knows all the moves. Chess is a good example where the object is to checkmate or capture the enemy king. One important feature of checkmates, especially in chess problem composition, is economy. This paper proposes a computational function to evaluate the economy of checkmate configurations on the chessboard. Several experiments were...

We consider dynamic electromagnetic evasion-interrogation games in which the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies to enhance detection. The resulting problem is formulated as a two-player zero-sum dynamic differential game in which the cost functional is based on the expected value of the...

We show that the following problem is EXP-complete: given a rational v and a two player, zero-sum Boolean gameG determine whether the value of G is at least v. The proof is via a translation of the proof of the same result for Boolean circuit games in [1]. 1 Preliminaries We will be using the encoding of [2] to replicate the proof of [1]. A familiarity with [2] will make the proof much easier t...

This paper investigates the problem of allocating multiple defensive resources to protect multiple sites against possible attacks by an adversary. The effectiveness of the resources in reducing potential damage to the sites is assumed to vary across the resources and across the sites and their availability is constrained. The problem is formulated as a two-person zero-sum game with piecewise li...