Pairwise interact-and-imitate dynamics

This paper introduces and studies a class of evolutionary dynamics—pairwise interact-and-imitate dynamics (PIID)—in which agents are matched in pairs, engage in a symmetric game, and imitate the opponent with a probability that depends on the difference in their payoffs. We provide a condition on the underlying game, named supremacy, and show that the population state in which all agents play the supreme strategy is globally asymptotically stable. We extend the framework to allow for payoff uncertainty, and check the robustness of our results to the introduction of some heterogeneity in the revision protocol followed by agents. Finally, we show that PIID can allow the survival of strictly dominated strategies, leads to the emergence of inefficient conventions in social dilemmas, and makes assortment ineffective in promoting cooperation.

If you could read my mind–an experimental beauty-contest game with children

We develop a new design for the experimental beauty-contest game (BCG) that is suitable for children in school age and test it with 114 schoolchildren aged 9–11 years as well as with adults. In addition, we collect a measure for cognitive skills to link these abilities with successful performance in the game. Results demonstrate that children can successfully understand and play a BCG. Choices start at a slightly higher level than those of adults but learning over time and depth of reasoning are largely comparable with the results of studies run with adults. Cognitive skills, measured as fluid IQ, are predictive only of whether children choose weakly dominated strategies but are neither associated with lower choices in the first round nor with successful performance in the BCG. In the implementation of our new design of the BCG with adults we find results largely in line with behavior in the classical BCG. Our new design for the experimental BCG allows to study the development of strategic interaction skills starting already in school age.

Pairwise Interact-and-Imitate Dynamics

This paper introduces and studies a class of evolutionary dynamics --- Pairwise Interact-and-Imitate Dynamics (PIID) --- in which agents are matched in pairs, engage in a symmetric game, and imitate the opponent with a probability that depends on the difference in their payoffs. We provide a condition on the underlying game, named supremacy, and show that the population state in which all agents play the supreme strategy is globally asymptotically stable. We extend the framework to allow for payoff uncertainty, and check the robustness of our results to the introduction of some heterogeneity in the revision protocol followed by agents. Finally, we show that PIID can allow the survival of strictly dominated strategies, leads to the emergence of inefficient conventions in social dilemmas, and makes assortment ineffective in promoting cooperation.

New expected impact functions and algorithms for modeling games under soft sets

Soft set is the power tool to deal with uncertainty in a parametric manner. In applications of soft set, one of the most important steps is to define mappings on soft sets. In this study, we model theory of game under theory of soft set which is an effective tool for handling uncertainties events and problems that may exist in a game. To this end, we first define some expected impact functions of players in soft games. Then, we propose three new decision making algorithms to solve the 2.2 × p, 2 . n × p and m . 2 × p soft matrix games, which cannot be settled by the relevant soft methods such as saddle points, lover and upper values, dominated strategies and Nash equilibrium. The proposed soft game algorithms are illustrated by examples.

A Modal Logic for Joint Abilities under Strategy Commitments

Representation and reasoning about strategic abilities has been an active research area in AI and multi-agent systems. Many variations and extensions of alternating-time temporal logic ATL have been proposed. However, most of the logical frameworks ignore the issue of coordination within a coalition, and are unable to specify the internal structure of strategies. In this paper, we propose JAADL, a modal logic for joint abilities under strategy commitments, which is an extension of ATL. Firstly, we introduce an operator of elimination of (strictly) dominated strategies, with which we can represent joint abilities of coalitions. Secondly, our logic is based on linear dynamic logic (LDL), an extension of linear temporal logic (LTL), so that we can use regular expressions to represent commitments to structured strategies. We analyze valid formulas in JAADL, give sufficient/necessary conditions for joint abilities, and show that model checking memoryless JAADL is in EXPTIME.

Nash versus coarse correlation

We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

Heuristic Voting as Ordinal Dominance Strategies

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply.To this end, we present a framework that allows for “shades of gray” of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.