Cooperative Games with Bounded Dependency Degree

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of cooperative games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we note that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games.Comment: 10 pages, full version of accepted AAAI-18 pape

Pure Nash Equilibria: Hard and Easy Games

We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is SigmaP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each players payoff depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players. The dependency structure of a game G can be expressed by a graph DG(G) or by a hypergraph H(G). By relating Nash equilibrium problems to constraint satisfaction problems (CSPs), we show that if G has small neighborhood and if H(G) has bounded hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems

Real Option Games with R&D and Learning Spillovers

We model pre-investment R&D decisions in the presence of spillover effects in an option pricing framework with analytic tractability. Two firms face two decisions that are solved for interdependently in a two-stage game. The first-stage decision is: what is the optimal level of coordination (optimal policy/technology choice)? The second-stage decision is: what is the optimal effort for a given level of the spillover effects and the cost of information acquisition? The framework is extended to a two-period stochastic game with (path-dependency inducing) switching costs that make strategy revisions harder. Strategy shifts are easier to observe in more volatile environments.Benefit Analysis; Real Options; Coordination Games; R&D

A Behavioral Approach to Learning in Economics - Towards an Economic Theory of Contingent Learning

In economics, adjustment of behavior has traditionally been treated as a "black box." Recent approaches that focus on learning behavior try to model, test, and simulate specific adjustment mechanisms in specific environments (mostly in games). Results often critically depend on distinctive assumptions, and are not easy to generalize. This paper proposes a different approach that aims to allow for more general conclusions in a methodologically more compatible way. It is argued that the introduction of the main determinants of learning behavior as situational restrictions into the standard economic model may be a fruitful way to capture some important aspects of human behavior that have often been omitted in economic theory. Based on a simple model of learning behavior (learning loop), robust findings from psychology are used to explain behavior adjustment, and to identify its determinants (contingent learning). An integrative methodology is proposed where the "black box" is not opened, but instead the factors that determine what happens inside, and the limits imposed by theses factors can be analyzed and used for model building. The paper concludes with testable hypotheses about learning behavior in the context of economics.microeconomics, game theory, learning theory, experiments

Social dilemmas in an online social network: the structure and evolution of cooperation

We investigate two paradigms for studying the evolution of cooperation--Prisoner's Dilemma and Snowdrift game in an online friendship network obtained from a social networking site. We demonstrate that such social network has small-world property and degree distribution has a power-law tail. Besides, it has hierarchical organizations and exhibits disassortative mixing pattern. We study the evolutionary version of the two types of games on it. It is found that enhancement and sustainment of cooperative behaviors are attributable to the underlying network topological organization. It is also shown that cooperators can survive when confronted with the invasion of defectors throughout the entire ranges of parameters of both games. The evolution of cooperation on empirical networks is influenced by various network effects in a combined manner, compared with that on model networks. Our results can help understand the cooperative behaviors in human groups and society.Comment: 14 pages, 7 figure