Complexity of Determining Nonemptiness of the Core

Coalition formation is a key problem in automated negotiation among self-interested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more efficiently. However, motivating the agents to abide to a solution requires careful analysis: only some of the solutions are stable in the sense that no group of agents is motivated to break off and form a new coalition. This constraint has been studied extensively in cooperative game theory. However, the computational questions around this constraint have received less attention. When it comes to coalition formation among software agents (that represent real-world parties), these questions become increasingly explicit. In this paper we define a concise general representation for games in characteristic form that relies on superadditivity, and show that it allows for efficient checking of whether a given outcome is in the core. We then show that determining whether the core is nonempty is $\mathcal{NP}$-complete both with and without transferable utility. We demonstrate that what makes the problem hard in both cases is determining the collaborative possibilities (the set of outcomes possible for the grand coalition), by showing that if these are given, the problem becomes tractable in both cases. However, we then demonstrate that for a hybrid version of the problem, where utility transfer is possible only within the grand coalition, the problem remains $\mathcal{NP}$-complete even when the collaborative possibilities are given

Punishment diminishes the benefits of network reciprocity in social dilemma experiments

Network reciprocity has been widely advertised in theoretical studies as one of the basic cooperation-promoting mechanisms, but experimental evidence favoring this type of reciprocity was published only recently. When organized in an unchanging network of social contacts, human subjects cooperate provided the following strict condition is satisfied: The benefit of cooperation must outweigh the total cost of cooperating with all neighbors. In an attempt to relax this condition, we perform social dilemma experiments wherein network reciprocity is aided with another theoretically hypothesized cooperation-promoting mechanism—costly punishment. The results reveal how networks promote and stabilize cooperation. This stabilizing effect is stronger in a smaller-size neighborhood, as expected from theory and experiments. Contrary to expectations, punishment diminishes the benefits of network reciprocity by lowering assortment, payoff per round, and award for cooperative behavior. This diminishing effect is stronger in a larger-size neighborhood. An immediate implication is that the psychological effects of enduring punishment override the rational response anticipated in quantitative models of cooperation in networks.We thank J. H. Lee for useful discussions. M.J. and Z.W. were, respectively, supported by the Research Grant Program of Inamori Foundation and the Chinese Young 1000 Talents Plan. B.P. received support from the Slovenian Research Agency (ARRS) and the Croatian Science Foundation through Projects J5-8236 and 5349, respectively. S.H. thanks the Israel-Italian collaborative project Network Cyber Security (NECST), Israel Science Foundation, Office of Naval Research (ONR), Japan Science Foundation, and the US-Israel Binational Science Foundation and the US National Science Foundation (BSF-NSF) for financial support. The Boston University Center for Polymer Studies is supported by NSF Grants PHY-1505000, CMMI-1125290, and CHE-1213217, by Defense Threat Reduction Agency (DTRA) Grant HDTRA1-14-1-0017, and by Department of Energy (DOE) Contract DE-AC07-05Id14517. (Inamori Foundation; Chinese Young 1000 Talents Plan; J5-8236 - Slovenian Research Agency (ARRS); 5349 - Croatian Science Foundation; Israel-Italian collaborative project Network Cyber Security (NECST); Israel Science Foundation; Office of Naval Research (ONR); Japan Science Foundation; US-Israel Binational Science Foundation; US National Science Foundation (BSF-NSF); PHY-1505000 - NSF; CMMI-1125290 - NSF; CHE-1213217 - NSF; HDTRA1-14-1-0017 - Defense Threat Reduction Agency (DTRA); DE-AC07-05Id14517 - Department of Energy (DOE))Published versio

Coalition Formation in Games without Synergies

This paper establishes sufficient conditions for the existence of a stable coalition structure in the ”coalition unanimity” game of coalition formation, first defined by Hart and Kurz (1983) and more recently studied by Yi (1997, 2000). Our conditions are defined on the strategic form game used to derive the payoffs the game of coalition formation. We show that if no synergies are generated by the formation of coalitions, a stable coalition structure always exists provided that players are symmetric and either the game exhibits strategic complementarity or, if strategies are substitutes, the best reply functions are contractions. We illustrate the role of synergies in a Cournot oligopoly example with cost reducing R&D.Coalition formation, Synergies, Strong Nash equilibrium

Coalition structure generation in cooperative games with compact representations

This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well

Extended Inclusive Fitness Theory bridges Economics and Biology through a common understanding of Social Synergy

Inclusive Fitness Theory (IFT) was proposed half a century ago by W.D. Hamilton to explain the emergence and maintenance of cooperation between individuals that allows the existence of society. Contemporary evolutionary ecology identified several factors that increase inclusive fitness, in addition to kin-selection, such as assortation or homophily, and social synergies triggered by cooperation. Here we propose an Extend Inclusive Fitness Theory (EIFT) that includes in the fitness calculation all direct and indirect benefits an agent obtains by its own actions, and through interactions with kin and with genetically unrelated individuals. This formulation focuses on the sustainable cost/benefit threshold ratio of cooperation and on the probability of agents sharing mutually compatible memes or genes. This broader description of the nature of social dynamics allows to compare the evolution of cooperation among kin and non-kin, intra- and inter-specific cooperation, co-evolution, the emergence of symbioses, of social synergies, and the emergence of division of labor. EIFT promotes interdisciplinary cross fertilization of ideas by allowing to describe the role for division of labor in the emergence of social synergies, providing an integrated framework for the study of both, biological evolution of social behavior and economic market dynamics.Comment: Bioeconomics, Synergy, Complexit

Coalitional Approaches to Collusive Agreements in Oligopoly Games.

In this paper we review a number of coalitional solution concepts for the analysis of the stability of cartels and mergers under oligopoly. We show that, although so far the industrial organization and the cooperative game-theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter-connected. We first consider the basic problem of the stability of the whole industry association of firms under oligopoly and, for this purpose, we introduce the concept of core in games with externalities. We show that different assumptions on the behaviour as well as on the timing of the coalitions of firms yield very di¤erent results on the set of allocations which are core-stable. We then consider the stability of associations of firms organized in coalition structures different from the grand coalition. To this end, various coalition formation games recently introduced by the so called endogenous coalition formation literature are critically reviewed. Again, di¤erent assumptions concerning the timing and the behaviout of firms are shown to yield a wide range of different results.Cooperative Games, Coalitions, Mergers, Cartels, Core, Games with Externalities, Endogenous Coalition Formation.

Insinking: A Methodology to Exploit Synergy in Transportation

vehicle routing;cooperative games;retailing;insinking;Shapley Monotonic Path;Logistic Service Providers