Multi-Round Cooperative Search Games with Multiple Players

Assume that a treasure is placed in one of M boxes according to a known distribution and that k searchers are searching for it in parallel during T rounds. We study the question of how to incentivize selfish players so that group performance would be maximized. Here, this is measured by the success probability, namely, the probability that at least one player finds the treasure. We focus on congestion policies C(l) that specify the reward that a player receives if it is one of l players that (simultaneously) find the treasure for the first time. Our main technical contribution is proving that the exclusive policy, in which C(1)=1 and C(l)=0 for l>1, yields a price of anarchy of (1-(1-{1}/{k})^{k})^{-1}, and that this is the best possible price among all symmetric reward mechanisms. For this policy we also have an explicit description of a symmetric equilibrium, which is in some sense unique, and moreover enjoys the best success probability among all symmetric profiles. For general congestion policies, we show how to polynomially find, for any theta>0, a symmetric multiplicative (1+theta)(1+C(k))-equilibrium. Together with an appropriate reward policy, a central entity can suggest players to play a particular profile at equilibrium. As our main conceptual contribution, we advocate the use of symmetric equilibria for such purposes. Besides being fair, we argue that symmetric equilibria can also become highly robust to crashes of players. Indeed, in many cases, despite the fact that some small fraction of players crash (or refuse to participate), symmetric equilibria remain efficient in terms of their group performances and, at the same time, serve as approximate equilibria. We show that this principle holds for a class of games, which we call monotonously scalable games. This applies in particular to our search game, assuming the natural sharing policy, in which C(l)=1/l. For the exclusive policy, this general result does not hold, but we show that the symmetric equilibrium is nevertheless robust under mild assumptions

Non-Cooperative Rational Interactive Proofs

Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to design protocols for computation outsourcing. Existing interactive-proof games largely fall into two categories: either as games of cooperation such as multi-prover interactive proofs and cooperative rational proofs, where the provers work together as a team; or as games of conflict such as refereed games, where the provers directly compete with each other in a zero-sum game. Neither of these extremes truly capture the strategic nature of service providers in outsourcing applications. How to design and analyze non-cooperative interactive proofs is an important open problem. In this paper, we introduce a mechanism-design approach to define a multi-prover interactive-proof model in which the provers are rational and non-cooperative - they act to maximize their expected utility given others\u27 strategies. We define a strong notion of backwards induction as our solution concept to analyze the resulting extensive-form game with imperfect information. We fully characterize the complexity of our proof system under different utility gap guarantees. (At a high level, a utility gap of u means that the protocol is robust against provers that may not care about a utility loss of 1/u.) We show, for example, that the power of non-cooperative rational interactive proofs with a polynomial utility gap is exactly equal to the complexity class P^{NEXP}

Joint Channel Selection and Power Control in Infrastructureless Wireless Networks: A Multi-Player Multi-Armed Bandit Framework

This paper deals with the problem of efficient resource allocation in dynamic infrastructureless wireless networks. Assuming a reactive interference-limited scenario, each transmitter is allowed to select one frequency channel (from a common pool) together with a power level at each transmission trial; hence, for all transmitters, not only the fading gain, but also the number of interfering transmissions and their transmit powers are varying over time. Due to the absence of a central controller and time-varying network characteristics, it is highly inefficient for transmitters to acquire global channel and network knowledge. Therefore a reasonable assumption is that transmitters have no knowledge of fading gains, interference, and network topology. Each transmitting node selfishly aims at maximizing its average reward (or minimizing its average cost), which is a function of the action of that specific transmitter as well as those of all other transmitters. This scenario is modeled as a multi-player multi-armed adversarial bandit game, in which multiple players receive an a priori unknown reward with an arbitrarily time-varying distribution by sequentially pulling an arm, selected from a known and finite set of arms. Since players do not know the arm with the highest average reward in advance, they attempt to minimize their so-called regret, determined by the set of players' actions, while attempting to achieve equilibrium in some sense. To this end, we design in this paper two joint power level and channel selection strategies. We prove that the gap between the average reward achieved by our approaches and that based on the best fixed strategy converges to zero asymptotically. Moreover, the empirical joint frequencies of the game converge to the set of correlated equilibria. We further characterize this set for two special cases of our designed game

Ms Pac-Man versus Ghost Team CEC 2011 competition

Games provide an ideal test bed for computational intelligence and significant progress has been made in recent years, most notably in games such as Go, where the level of play is now competitive with expert human play on smaller boards. Recently, a significantly more complex class of games has received increasing attention: real-time video games. These games pose many new challenges, including strict time constraints, simultaneous moves and open-endedness. Unlike in traditional board games, computational play is generally unable to compete with human players. One driving force in improving the overall performance of artificial intelligence players are game competitions where practitioners may evaluate and compare their methods against those submitted by others and possibly human players as well. In this paper we introduce a new competition based on the popular arcade video game Ms Pac-Man: Ms Pac-Man versus Ghost Team. The competition, to be held at the Congress on Evolutionary Computation 2011 for the first time, allows participants to develop controllers for either the Ms Pac-Man agent or for the Ghost Team and unlike previous Ms Pac-Man competitions that relied on screen capture, the players now interface directly with the game engine. In this paper we introduce the competition, including a review of previous work as well as a discussion of several aspects regarding the setting up of the game competition itself. © 2011 IEEE