Smoothed Efficient Algorithms and Reductions for Network Coordination Games

Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case. This is a potential game where the sequential-better-response algorithm is known to converge to a pure NE, albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial) smoothed complexity when the underlying game graph is a complete (resp. arbitrary) graph, and every player has constantly many strategies. We note that the complete graph case is reminiscent of perturbing all parameters, a common assumption in most known smoothed analysis results. Second, we define a notion of smoothness-preserving reduction among search problems, and obtain reductions from $2$-strategy network coordination games to local-max-cut, and from $k$-strategy games (with arbitrary $k$) to local-max-cut up to two flips. The former together with the recent result of [BCC18] gives an alternate $O(n^8)$-time smoothed algorithm for the $2$-strategy case. This notion of reduction allows for the extension of smoothed efficient algorithms from one problem to another. For the first set of results, we develop techniques to bound the probability that an (adversarial) better-response sequence makes slow improvements on the potential. Our approach combines and generalizes the local-max-cut approaches of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful definition of the matrix which captures the increase in potential, a tighter union bound on adversarial sequences, and balancing it with good enough rank bounds. We believe that the approach and notions developed herein could be of interest in addressing the smoothed complexity of other potential and/or congestion games

Evolutionary Stability in Common Pool Resources.

The Tragedy of the Commons refers to the dissipation of a common- pool ressource when any appropriator has free access to it. Under the behavior of absolute payoff maximisation, the common-pool resource game leads to a Nash equilibrium in which the resource is overexploited. However, some empirical studies show that the overutilization is even larger than the Nash equilibrium predicts. We account for these results in an evolutionary framework. Under an imitation-experimentation dynamics, the long run stable behavior implies a larger exploitation of the resource than in the classical Nash equilibrium.common-pool resource, imitation behavior, evolutionary stable strategy, evolutionary games.

Interaction and imitation in a world of Quixotes and Sanchos

Producción CientíficaThis paper studies a two-population evolutionary game in a new setting in between a symmetric and an asymmetric evolutionary model. It distinguishes two types of agents: Sanchos, whose payoffs are defined by a prisoner’s dilemma game, and Quixotes, whose payoffs are defined by a snowdrift game. Considering an imitative revision protocol, a revising agent is paired with someone from his own population or the other population. When matched, they observe payoffs, but not identities. Thus, agents in one population interact and imitate agents from their own population and from the other population. In this setting we prove that a unique mixed-strategy asymptotically stable fixed point of the evolutionary dynamics exists. Taking as an example the compliance with social norms, and depending on the parameters, two type of equilibrium are possible, one with full compliance among Quixotes and partial compliance among Sanchos, or another with partial compliance among Quixotes and defection among Sanchos. In the former type, Sanchos comply above their Nash equilibrium (as they imitate compliant Quixotes). In the latter type, Quixotes comply below their Nash equilibrium (as they imitate defecting Sanchos)

Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games

For a class of n-player (n ? 2) sequential bargaining games with probabilistic recognition and general agreement rules, we characterize pure strategy Stationary Subgame Perfect (PSSP) equilibria via a finite number of equalities and inequalities. We use this characterization and the degree theory of Shannon, 1994, to show that when utility over agreements has negative definite second (contingent) derivative, there is a finite number of PSSP equilibrium points for almost all discount factors. If in addition the space of agreements is one-dimensional, the theorem applies for all SSP equilibria. And for oligarchic voting rules (which include unanimity) with agreement spaces of arbitrary finite dimension, the number of SSP equilibria is odd and the equilibrium correspondence is lower-hemicontinuous for almost all discount factors. Finally, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.Local Uniqueness of Equilibrium, Regularity, Sequential Bargaining.

Peer Prediction for Learning Agents

Peer prediction refers to a collection of mechanisms for eliciting information from human agents when direct verification of the obtained information is unavailable. They are designed to have a game-theoretic equilibrium where everyone reveals their private information truthfully. This result holds under the assumption that agents are Bayesian and they each adopt a fixed strategy across all tasks. Human agents however are observed in many domains to exhibit learning behavior in sequential settings. In this paper, we explore the dynamics of sequential peer prediction mechanisms when participants are learning agents. We first show that the notion of no regret alone for the agents' learning algorithms cannot guarantee convergence to the truthful strategy. We then focus on a family of learning algorithms where strategy updates only depend on agents' cumulative rewards and prove that agents' strategies in the popular Correlated Agreement (CA) mechanism converge to truthful reporting when they use algorithms from this family. This family of algorithms is not necessarily no-regret, but includes several familiar no-regret learning algorithms (e.g multiplicative weight update and Follow the Perturbed Leader) as special cases. Simulation of several algorithms in this family as well as the $\epsilon$-greedy algorithm, which is outside of this family, shows convergence to the truthful strategy in the CA mechanism.Comment: 34 pages, 9 figure

Overview English Asa Second Language for Young Learners

Young learners have special charactheristics hence the teachers of English as a Second language needs special strategy too. It is indicated that the increas of abilities to learn second language is started from the early age. We can imagine when the teachers do not use and apply appropriate teaching methods and strategy in teaching English for young learners. As a result, the students' achievement does not work well. Thus, except to be successful in teaching English for young learners, it is very necessary for teachers to understand the characteristics of young learners.' Learning method s will influence how a teacher makes a lesson plan according to young learners' minds. This article tries to explain some methods of young learners in teaching English as a second language for young learner

Inducing a self-fulfilling prophecy in public goods games

This study explores how a self-fulfilling prophecy can solve a social dilemma. We ran two experimental treatments, baseline and automata. Both consisted of a finitely repeated public goods game with a surprise restart. In the automata treatment it was announced that there might be automata playing a grim trigger strategy. This announcement became a self-fulfilling prophecy. That is, most participants actually followed a grim trigger strategy in the automata treatment resulting on an increase on the average contributions to the public good relative to the baseline treatment. Moreover, four out of nine groups managed to fully cooperate almost until the last period. Furthermore, after the surprise restart, when the automata threat is less credible, subjects’ behavior was very close to that in the original game