717 research outputs found
The Quality of Equilibria for Set Packing Games
We introduce set packing games as an abstraction of situations in which
selfish players select subsets of a finite set of indivisible items, and
analyze the quality of several equilibria for this class of games. Assuming
that players are able to approximately play equilibrium strategies, we show
that the total quality of the resulting equilibrium solutions is only
moderately suboptimal. Our results are tight bounds on the price of anarchy for
three equilibrium concepts, namely Nash equilibria, subgame perfect equilibria,
and an equilibrium concept that we refer to as -collusion Nash equilibrium
ENDOGENOUS MOVE STRUCTURE AND VOLUNTARY PROVISION OF PUBLIC GOODS: THEORY AND EXPERIMENT
In this paper we examine voluntary contributions to a public good, embedding Varian (1994)’s voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian’s model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.Public Goods, Voluntary Contributions, Sequential Contributions, Endogenous Timing, Action Commitment, Observable Delay, Experiment
Efficient Equilibria in Polymatrix Coordination Games
We consider polymatrix coordination games with individual preferences where
every player corresponds to a node in a graph who plays with each neighbor a
separate bimatrix game with non-negative symmetric payoffs. In this paper, we
study -approximate -equilibria of these games, i.e., outcomes where
no group of at most players can deviate such that each member increases his
payoff by at least a factor . We prove that for these
games have the finite coalitional improvement property (and thus
-approximate -equilibria exist), while for this
property does not hold. Further, we derive an almost tight bound of
on the price of anarchy, where is the number of
players; in particular, it scales from unbounded for pure Nash equilibria ( to for strong equilibria (). We also settle the complexity
of several problems related to the verification and existence of these
equilibria. Finally, we investigate natural means to reduce the inefficiency of
Nash equilibria. Most promisingly, we show that by fixing the strategies of
players the price of anarchy can be reduced to (and this bound is tight)
Abstracting Imperfect Information Away from Two-Player Zero-Sum Games
In their seminal work, Nayyar et al. (2013) showed that imperfect information
can be abstracted away from common-payoff games by having players publicly
announce their policies as they play. This insight underpins sound solvers and
decision-time planning algorithms for common-payoff games. Unfortunately, a
naive application of the same insight to two-player zero-sum games fails
because Nash equilibria of the game with public policy announcements may not
correspond to Nash equilibria of the original game. As a consequence, existing
sound decision-time planning algorithms require complicated additional
mechanisms that have unappealing properties. The main contribution of this work
is showing that certain regularized equilibria do not possess the
aforementioned non-correspondence problem -- thus, computing them can be
treated as perfect information problems. Because these regularized equilibria
can be made arbitrarily close to Nash equilibria, our result opens the door to
a new perspective on solving two-player zero-sum games and, in particular,
yields a simplified framework for decision-time planning in two-player zero-sum
games, void of the unappealing properties that plague existing decision-time
planning approaches
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}
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