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on Game Theory |
| By: | Trudeau, Christian; Vidal-Puga, Juan |
| Abstract: | We introduce a new family of cooperative games for which there is coincidence between the nucleolus and the Shapley value. These so-called clique games are such that agents are divided into cliques, with the value created by a coalition linearly increasing with the number of agents belonging to the same clique. Agents can belong to multiple cliques, but for a pair of cliques, at most a single agent belong to their intersection. Finally, if two agents do not belong to the same clique, there is at most one way to link the two agents through a chain of agents, with any two non-adjacent agents in the chain belonging to disjoint sets of cliques. We provide multiple examples for clique games. Graph-induced games, either when the graph indicates cooperation possibilities or impossibilities, provide us with opportunities to confirm existing results or discover new ones. A particular focus are the minimum cost spanning tree problems. Our result allows us to obtain new coincidence results between the nucleolus and the Shapley value, as well as other cost sharing methods for the minimum cost spanning tree problem. |
| Keywords: | nucleolus; Shapley value; clique; minimum cost spanning tree |
| JEL: | C71 |
| Date: | 2018–11–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96710&r=all |
| By: | Ngo Van Long |
| Abstract: | The purpose of this paper is to model the influence of Kantian moral scruples in a dynamic environment. Our objectives are two-fold. Firstly, we investigate how a Nash equilibrium among agents who have moral scruples may ensure that the exploitation of a common property renewable resource is Pareto efficient at every point of time. Secondly, we outline a prototype model that shows, in an overlapping generation framework, how a community’s sense of morality may evolve over time and identifies conditions under which the community may reach a steady state level of morality in which everyone is perfectly Kantian. |
| Keywords: | tragedy of the commons, dynamic games, Nash equilibrium, self-image, categorical imperative |
| JEL: | C71 D62 D71 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7880&r=all |
| By: | René van den Brink (Department of Econometrics and Tinbergen Institute, VU University Amsterdam); Dinko Dimitrov (Chair of Economic Theory - Saarland University); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne, PSE-CNRS, Université Paris 1) |
| Abstract: | We study the issue of assigning weights to players that identify winning coalitions in plurality voting democracies. For this, we consider plurality games which are simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be precisely supportive if it possible to assign weights to players in such a way that a coalition being winning in a partition implies that the combined weight of its members is maximal over all coalitions in the partition. A plurality game is decisive if in every partition there is exactly one winning coalition. We show that decisive plurality games with at most four players, majority games with an arbitrary number of players, and almost symmetric decisive plurality games with an arbitrary number of players are precisely supportive. Complete characterizations of a partition's winning coalitions are provided as well |
| Keywords: | plurality game; plurality voting; precise support; simple game in partition function form; winning coalition |
| JEL: | C71 D62 D72 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:19018&r=all |
| By: | Joaquín Gómez-Miñambres (Lafayette College, Department of Economics; Economic Science Institute, Chapman University); Eric Schniter (Economic Science Institute, Chapman University; Argyros School of Business and Economics, Chapman University); Timothy W. Shields (Economic Science Institute, Chapman University; Argyros School of Business and Economics, Chapman University) |
| Abstract: | While many economic interactions feature “All-or-Nothing” options nudging investors towards going “all-in”, such designs may unintentionally affect reciprocity. We manipulate the investor’s action space in two versions of the “trust game”. In one version investors can invest either “all” their endowment or “nothing”. In the other version, they can invest any amount of the endowment. Consistent with our intentions-based model, we show that "all-or-nothing” designs coax more investment but limit investors’ demonstrability of intended trust. As a result, “all-in” investors are less generously reciprocated than when they can invest any amount, where full investments are a clearer signal of trustworthiness. |
| JEL: | C72 C90 C91 D63 D64 L51 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:19-24&r=all |
| By: | Banchongsan Charoensook (Keimyung University, Keimyung Adams College, Department of International Business) |
| Abstract: | In this note, I study the roles of value heterogeneity - i.e., agents are heterogeneous in terms of values of nonrival information thay they possessed - in determining the shapes of two-way flow Strict Nash networks when small amount of decay is present. I do so by extending the two-way flow network with small decay of De Jaegher and Kamphorst (J ECON BEHAV ORGAN, 2015). Results of this extension shows that the effects of value heterogeneity on Strict Nash networks, when small decay is present, largely resemble the effects of heterogeneity in link formation cost - without decay - found in the literature. Another surprising finding is that value heterogeneity can extend the diameters of Strict Nash networks without changing any other properties. In the discussion section of this note, I relate this finding to two well-known concepts in the studies of social networks - small world and preferential attachment. |
| Keywords: | Network Formation, Strict Nash Network, Two-way Flow Network, Branching Network |
| JEL: | C72 D85 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2019.20&r=all |
| By: | Robert P. Gilles |
| Abstract: | This survey explores the literature on game-theoretic models of network formation under the hypothesis of mutual consent in link formation. The introduction of consent in link formation imposes a coordination problem in the network formation process. This survey explores the conclusions from this theory and the various methodologies to avoid the main pitfalls. The main insight originates from Myerson's work on mutual consent in link formation and his main conclusion that the empty network (the network without any links) always emerges as a strong Nash equilibrium in any game-theoretic model of network formation under mutual consent and positive link formation costs. Jackson and Wolinsky introduced a cooperative framework to avoid this main pitfall. They devised the notion of a pairwise stable network to arrive at equilibrium networks that are mainly non-trivial. Unfortunately, this notion of pairwise stability requires coordinated action by pairs of decision makers in link formation. I survey the possible solutions in a purely non-cooperative framework of network formation under mutual consent by exploring potential refinements of the standard Nash equilibrium concept to explain the emergence of non-trivial networks. This includes the notions of unilateral and monadic stability. The first one is founded on advanced rational reasoning of individuals about how others would respond to one's efforts to modify the network. The latter incorporates trusting, boundedly rational behaviour into the network formation process. The survey is concluded with an initial exploration of external correlation devices as an alternative framework to address mutual consent in network formation. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.11693&r=all |
| By: | Eibelshäuser, Steffen; Poensgen, David |
| JEL: | C63 C73 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc19:203603&r=all |
| By: | JORGE OMAR RAZO-DE ANDA (INSTITUTO POLITÉCNICO NACIONAL); ANA CECILIA PARADA-ROJAS (INSTITUTO POLITÉCNICO NACIONAL); SALVADOR CRUZ-AKÉ (INSTITUTO POLITÉCNICO NACIONAL) |
| Abstract: | Minsky's idea of triggering a financial crisis is the adoption of risky financial positions by companies and their relationship with the financial system through banks and the credit they provide. The present work seeks to provide an explanation from a microeconomic point of view through the behavior of agents and their decision making under a Theory of evolutionary games, especially population games. The great advantage of this type of games is that it allows us to obtain proportions of the different decisions that a population or subpopulation is taking and how their interaction promotes equilibrium and the dynamics towards (or around) them.This allows us to determine the dynamics and equilibria of the credit cycle, following Minsky's idea of financial fragility. Additionally, the dynamics of the replicator allows transforming the differential equations in a Lotka-Volterra system, from which it can be concluded that both companies and banks adopt a predatory prey relationship in order to survive. |
| Keywords: | Capital Structure, Evolutionary Games, Financial crises |
| JEL: | C73 G02 G01 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:sek:iacpro:9110841&r=all |
| By: | Bauer, Dominik; Wolff, Irenaeus |
| JEL: | C72 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc19:203601&r=all |
| By: | Martin Frank; Michael Herty; Torsten Trimborn |
| Abstract: | Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this work, we derive mean field game partial differential equation systems from deterministic microscopic agent dynamics. The dynamics are given by a particular class of ordinary differential equations, for which an optimal strategy can be computed (Bressan, Milan Journal of Mathematics, 2011). We use the concept of Nash equilibria and apply the dynamic programming principle to derive the mean field limit equations and we study the scaling behavior of the system as the number of agents tends to infinity and find several mean field game limits. Especially we avoid in our derivation the notion of measure derivatives. Novel scales are motivated by an example of an agent-based financial market model. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.13534&r=all |
| By: | V\'itor V. Vasconcelos; Phillip M. Hannam; Simon A. Levin; Jorge M. Pacheco |
| Abstract: | While the benefits of common and public goods are shared, they tend to be scarce when contributions are provided voluntarily. Failure to cooperate in the provision or preservation of these goods is fundamental to sustainability challenges, ranging from local fisheries to global climate change. In the real world, such cooperative dilemmas occur in multiple interactions with complex strategic interests and frequently without full information. We argue that voluntary cooperation enabled across multiple coalitions (akin to polycentricity) not only facilitates greater generation of non-excludable public goods, but may also allow evolution toward a more cooperative, stable, and inclusive approach to governance. Contrary to any previous study, we show that these merits of multi-coalition governance are far more general than the singular examples occurring in the literature, and are robust under diverse conditions of excludability, congestability of the non-excludable public good, and arbitrary shapes of the return-to-contribution function. We first confirm the intuition that a single coalition without enforcement and with players pursuing their self-interest without knowledge of returns to contribution is prone to cooperative failure. Next, we demonstrate that the same pessimistic model but with a multi-coalition structure of governance experiences relatively higher cooperation by enabling recognition of marginal gains of cooperation in the game at stake. In the absence of enforcement, public-goods regimes that evolve through a proliferation of voluntary cooperative forums can maintain and increase cooperation more successfully than singular, inclusive regimes. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.11337&r=all |
| By: | Russell Golman; Aditi Jain; Sonica Saraf |
| Abstract: | Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of social identity expression based on the opposing, but not mutually exclusive, motives to conform and to be unique among one's neighbors in a social network. We then model the social dynamics that arise from these motives. We find that the dynamics typically enter random walks or stochastic limit cycles rather than converging to a static equilibrium. We also prove that without social network structure or, alternatively, without the uniqueness motive, reasonable adaptive dynamics would necessarily converge to equilibrium. Thus, we show that nuanced psychological assumptions (recognizing preferences for uniqueness along with conformity) and realistic social network structure are both necessary for explaining how complex, unpredictable cultural trends emerge. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.13385&r=all |
| By: | Mauersberger, Felix |
| JEL: | C91 C92 D84 E37 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc19:203600&r=all |
| By: | Eray Turkel; Yunus C. Aybas |
| Abstract: | Persuasion is an exceedingly difficult task. A leading cause of this difficulty is the misalignment of preferences, which is studied extensively by the literature on persuasion games. However, the difficulty of communication also has a first order effect on outcomes and welfare of agents. Motivated by this observation, we study a model of Bayesian persuasion in which the communication between the sender and the receiver is constrained. We limit the cardinality of the signal space to be less than the cardinality of the action space and the state space. This limits the sender's ability of making arbitrarily many action recommendations. We prove the existence of a solution to the sender's utility maximization problem and characterize its properties. In solving this problem, we develop a novel approach for solving Bayesian persuasion problems, which can be applied to a wide range of settings. We characterize the sender's willingness to pay for an additional signal as a function of the prior belief, which we interpret as the value of precise communication. We show that increased precision might not be always welfare improving by showing that the receiver might prefer coarse communication. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.13547&r=all |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Fen Li (Centre d'Economie de la Sorbonne) |
| Abstract: | We provide a detailed study of the threshold model, where both conformist and anti-conformist agents coexist. Our study bears essentially on the convergence of the opinion dynamics in the society of agents, i.e., finding absorbing classes, cycles, etc. Also, we are interested in the existence of cascade effects, as this may constitute a undesirable phenomenon in collective behavior. We divide our study into two parts. In the first one, we basically study the threshold model supposing a fixed complete network, where every one is connected to every one, like in the seminal work of Granovetter. We study the case of a uniform distribution of the threshold, of a Gaussian distribution and finally give a result for arbitraty distributions, supposing there is one type of anti-conformist. In a second part, the graph is no more complete and we suppose that the neighborhood of an agent is random, drawn at each time step from a distribution. We distinguish the case where the degree (number of links) of an agent is fixed, and where there is an arbitrary degree distribution. We show the existence of cascades and that for most societies, the opinion converges to a chaotic situation |
| Keywords: | threshold model; anti-conformism; absorbing class; opinion dynamics |
| JEL: | C7 D7 D85 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:19016&r=all |
| By: | Shaofei Jiang |
| Abstract: | This paper studies disclosure games with general disclosure rules. A sender observes a piece of evidence about an unknown state and tries to influence the posterior belief of a receiver by disclosing evidence with possible omission. We characterize the unique equilibrium value function of the sender given any disclosure rule. Applying this characterization, we study left-censored disclosure, where evidence is a sequence of signals, and the sender can truncate evidence from the left. In equilibrium, seemingly sub-optimal messages are disclosed, and the sender's disclosure contains the longest truncation that yields the maximal difference between the number of favorable and unfavorable signals. These findings are results of coordination among senders with different evidence endowment. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.13633&r=all |
| By: | J. Atsu Amegashie |
| Abstract: | There are several empirical studies of ex post analysis of citations in academia. There is no ex ante analysis of citations. I consider a game-theoretic model of a contest between scholars on the basis of two widely-used measures of citations (i.e., the ℎ-index and total citation count) and the newly-developed Euclidean index (Perry and Reny, American Economic Review, 2016). I find equilibria in which there are more and better-quality papers in the total citations contest than in the ℎ-index contest. When the marginal cost of effort is constant, the scholars are indifferent between the number of papers and the quality of papers in the total citations contest but prefer quality of papers in the Euclidean contest although the total number of citations is the same in both contests. In some cases, the total citations contest yields the same quality of papers but more papers than the Euclidean contest, a result which holds when the marginal cost of effort is increasing but is not possible when the marginal cost of effort is constant. Consistent with previous empirical results, I find that as the cost of writing a paper increases, the ℎ-index is inferior to the total citations index in both the quality and quantity of papers. This result is driven by how the cost of effort constrains the number of papers that a scholar can write and how the number of papers, in turn, constrains how the ℎ-index counts citations. |
| Keywords: | citation count, contests, Euclidean index, ℎ-index, integer programming game |
| JEL: | D72 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7890&r=all |
| By: | Ott, Marion |
| JEL: | D44 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc19:203616&r=all |
| By: | Swagata Bhattacharjee (Ashoka University) |
| Abstract: | This paper explores a potentially important role of delegation: as a signal to sustain cooperation in coordination games. I consider a static principal-agent model with two tasks, one of which requires cooperation between the principal and the agent. If there is asymmetric information about the agent's type, the principal with a private belief that the agent is a good type can delegate the first task as a signal of his private belief. This equilibrium is supported by the forward induction argument. I conduct laboratory experiments to test these theoretical predictions and to examine the role of information in equilibrium selection. I find that delegation is used only sometimes to facilitate cooperation; however, when the subjects have information about past sessions, there is a statistically significant increase in the use of delegation. This evidence suggests that information matters in equilibrium selection in Bayesian games. |
| Keywords: | Delegation, Forward Induction, Lab Experiment, Information |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:17&r=all |