nep-gth New Economics Papers
on Game Theory
Issue of 2018‒03‒12
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Whom can you trust? Reputation and Cooperation in Networks By Maia King;
  2. Bargaining Foundation for Ratio Equilibrium in Public Good Economies By Anne van den Nouweland; Agnieszka Rusinowka
  3. On Existence of a Global Games Equilibrium Selection By Eric J. Hoffmann; Tarun Sabarwal
  4. Opinion formation and targeting when persuaders have extreme and centrist opinions By Agnieszka Rusinowka; Akylai Taalaibekova
  5. The Multiplier Effect in Two-Sided Markets with Bilateral Investments By Deniz Dizdar; Benny Moldovanu; Nora Szech
  6. A case of evolutionary stable attainable equilibrium in the lab By Christoph Kuzmics; Daniel Rodenburger
  7. Public Goods Provision with Rent-Extracting Administrators By Tobias Cagala; Ulrich Glogowsky; Veronika Grimm; Johannes Rincke
  8. Nudges in network By Benjamin Ouvrard; Anne Stenger
  9. The effects of physical activity on social interactions: The case of trust and trustworthiness By Di Bartolomeo Giovanni; Stefano Papa
  10. Bargaining and the role of negotiators' competitiveness By Keser, Claudia; Müller, Stephan; Peterlé, Emmanuel; Rau, Holger A.
  11. Beating the Matthew Effect: Head Starts and Catching Up in a Dynamic All-Pay Auction* By Clark, Derek J.; Nilssen, Tore
  12. Achieving perfect coordination amongst agents in the co-action minority game By Hardik Rajpal; Deepak Dhar
  13. A Note on Ex-Ante Stable Lotteries By Schlegel, J. C.
  14. Neutral candidates in approval and disapproval vote By González, Stéphane; Laruelle, Annick; Solal, Philippe
  15. Existence and Optimality of Cournot-Nash Equilibria in a Bilateral Oligopoly with Atoms and an Atomless Part By Francesca Busetto; Giulio Codognato; Sayantan Ghosal; Ludovic A. Julien; Simone Tonin
  16. Global climate change mitigation: Strategic incentives By Sigit Perdana; Rod Tyers
  17. The Big Match with a Clock and a Bit of Memory By Kristoffer Arnsfelt Hansen; Rasmus Ibsen-Jensen; Abraham Neyman
  18. Naked exclusion under exclusive-offer competition By Hiroshi Kitamura; Noriaki Matsushima; Misato Sato
  19. A Network Approach to Public Goods By Elliott, M.; Golub, B.
  20. Collusion in Two-Sided Markets By Lefouili, Yassine; Pinho, Joana
  21. Does the Potential to Merge Reduce Competition? By Hackbarth, Dirk; Taub, Bart

  1. By: Maia King (Queen Mary University of London (PhD candidate), University of Oxford);
    Abstract: Community enforcement is an important device for sustaining efficiency in some repeated games of cooperation. We investigate cooperation when information about players' reputations spreads to their future partners through links in a social network that connects them. We nd that information supports cooperation by increasing trust between players, and obtain the `radius of trust': an endogenous network listing the potentially cooperative relationships between pairs of players in a community. We identify two aspects of trust, which relate to the network structure in different ways. Where trust depends on the shadow of punishment, players are trusted if others can communicate about them. This is linked to 2-connectedness of the network and the length of cycles within it. Where trust relates to knowledge of a player's type, players are trusting if they are more likely to receive information through their network connections. Both aspects of trust are linked to new centrality measures that we construct from the probabilities of node-to-node information transmission in networks, for which we provide a novel and simple method of calculation.
    Keywords: Cooperation, community enforcement, information transmission, networks, im-perfect private monitoring, repeated games, reputation, trust
    JEL: C73 D83 D85 L14 Z13
    Date: 2017–12–12
  2. By: Anne van den Nouweland (University of Oregon - Department of Economics); Agnieszka Rusinowka (Centre d'Economie de la Sorbonne - Paris School of Economics)
    Abstract: We provide a bargaining foundation for the concept of ratio equilibrium in public good economies. We define a bargaining game of alternating offers in which players bargain to determine their cost shares of public good production and a level of public good. We study the stationary subgame perfect equilibrium without delay of the bargaining game. We demonstrate that when the players are perfectly patient, they are indifferent between the equilibrium offers of all players. We also show that every stationary subgame perfect equilibrium without delay in which the ratios offered by all players are the same leads to a ratio equilibrium. In addition, we demonstrate that all equilibrium ratios are offered by the players at some stationary subgame perfect equilibrium without delay. We use these results to discuss the case when the assumption of perfectly patient players is relaxed and the cost of delay vanishes
    Keywords: ratio equilibrium; public good economy; bargaining game; stationary subgame perfect equilibrium
    JEL: H41 D7
    Date: 2018–02
  3. By: Eric J. Hoffmann (West Texas A&M University); Tarun Sabarwal (Department of Economics, The University of Kansas;)
    Abstract: We formulate a model of a global game that allows for arbitrary strategic interaction, and we prove existence of a global games equilibrium selection in this model. This shows that the global games method is well-defined in a large class of global games, thus providing a foundation for the study of their equilibrium behavior, especially as research in global games moves beyond cases with strategic complements. We also show that in every global game, even though the information of each player is correlated, the joint information measure is absolutely continuous with respect to the product of its marginals. In particular, the result here can be used to show that there is a global games equilibrium selection in the finite-player version of the model in Karp, Lee, and Mason (2007), thus addressing a gap in the proof of equilibrium existence documented in Hoffmann and Sabarwal (2015).
    Keywords: Global games, strategic complements, strategic substitutes, strategic heterogeneity, monotone games, equilibrium selection Women’s Health, Preventive Care, Ethnicity
    JEL: C70 C72 C73
    Date: 2017–02
  4. By: Agnieszka Rusinowka (Centre d'Economie de la Sorbonne - Paris School of Economics); Akylai Taalaibekova (CORE - Université Catholique de Louvain and Centre d'Economie de la Sorbonne)
    Abstract: We consider a model of competitive opinion formation in which three persuaders characterized by (possibly unequal) persuasion impacts try to influence opinions in a society of individuals embedded in a social network. Two of the persuaders have the extreme and opposite opinions, and the third one has the centrist opinion. Each persuader chooses one individual to target, i.e., he forms a link with the chosen individual in order to spread his own “point of view” in the society and to get the average long run opinion as close as possible to his own opinion. We examine the opinion convergence and consensus reaching in the society. We study the existence and characterization of pure strategy Nash equilibria in the game played by the persuaders with equal impacts. This characterization depends on influenceability and centrality (intermediacy) of the targets. We discuss the effect of the centrist persuader on the consensus and symmetric equilibria, compared to the framework with only two persuaders having the extreme opinions. When the persuasion impacts are unequal with one persuader having a sufficiently large impact, the game has only equilibria in mixed strategies
    Keywords: social network; opinion formation; consensus; targeting; lobbying; extreme and centrist persuaders
    JEL: D85 D72 C72
    Date: 2018–02
  5. By: Deniz Dizdar; Benny Moldovanu; Nora Szech
    Abstract: Agents in a finite two-sided market are matched assortatively, based on costly investments. Besides signaling private, complementary types, investments generate direct benefits for partners. We explore quantitative properties of the equilibrium investment behavior. The bilateral external benefits induce an investment multiplier effect. This multiplier effect depends in a complex way on agents’ uncertainty about their own rank and about the types and investments of potential partners. We characterize how the multiplier effect hinges on market size, and how it interacts with other important factors such as the costs of investment and the signaling incentives induced by competition.
    Keywords: matching, signaling, investment, multiplier effect
    JEL: C78 D44 D82
    Date: 2017
  6. By: Christoph Kuzmics (University of Graz, Austria); Daniel Rodenburger (University of Jena, Germany)
    Abstract: We reinvestigate data from a 14-player voting game experiment by Forsythe, Myerson, Rietz, and Weber (1993). Performing a powerful test, we find that the hypothesis of evolutionary stable attainable Nash equilibrium play in this complicated game cannot be rejected if we account for risk aversion, calibrated in another treatment (p-value 0.7799 with a sample size of 384).
    Keywords: Opinion polls; Elections; Voting; Testing; Nash equilibrium; Attainable equilibrium; Symmetries
    JEL: C52 C72 D72
    Date: 2018–02
  7. By: Tobias Cagala; Ulrich Glogowsky; Veronika Grimm; Johannes Rincke
    Abstract: This paper studies public goods provision in an experiment in which contributors repeatedly interact with rent-extracting administrators. Our main result is that the presence of an administrator reduces contributions but only because rent extraction lowers the MPCR. Analysing the dynamic interactions between the contributors and the administrator, we demonstrate that rent-extraction and cooperation shocks trigger short-run adjustments in the agents’ behaviour. However, shocks do not have permanent effects. This explains the long-run resilience of cooperation to rent extraction. We also show that cooperative attitudes and trust are traits that explain permanent differences in the short-run volatility of public goods provision.
    Keywords: cooperation, rent extraction, corruption, trustworthiness, public goods, public trust game, panel vector autoregressive model
    JEL: C32 C91 C92 H41
    Date: 2017
  8. By: Benjamin Ouvrard (UMR INRA – AgroParisTech, Laboratoire d’Economie Forestière, 54042 Nancy Cedex, France); Anne Stenger (UMR INRA – AgroParisTech, Laboratoire d’Economie Forestière, 54042 Nancy Cedex, France; Department of Economics, BETA-CNRS, University of Strasbourg, 61, avenue de la Forêt Noire 67085 Strasbourg Cedex)
    Abstract: This paper presents a model of voluntary contributions for a local public good, with individuals in a fixed network (complete, circle, line and star), based on the model of Bramoulle and Kranton (2007). We first characterize the equilibrium conditions in the absence of external incentives. We then consider the introduction of an informational nudge (announcement of the socially optimal contribution), both under complete and incomplete information regarding individuals' positions in the network. We show that, regardless of the regulator's level of information, an informational nudge may induce higher levels of aggregate contributions in circle and complete networks, and reduces strategic uncertainty, as long as individuals' sensitivity to the nudge (or their interest in the public good that is provided) is high enough. However, in star and line networks, the level of information available to the contributions or reduce strategic uncertainty. Our main conclusion is therefore that a nudge policy should target specific individuals in specific networks. Moreover, we consider a "second best" nudge for line networks under incomplete information because the socially efficient profile of contributions may be complex to implement in such a situation.
    Keywords: nudge; network, local public goods, information disclosure
    JEL: C72 D83 H41
    Date: 2017–02
  9. By: Di Bartolomeo Giovanni; Stefano Papa
    Abstract: There is no doubt that physical activity improves health conditions; however, does it also affect the way people interact? Beyond the obvious effects related to team games or sharing common activities such as attending a gym, we wonder whether physical activity has in itself some effect on social behavior. Our research focuses on the potential effects of physical activity on trust and trustworthiness. Specifically, we compare the choices of subjects playing an investment game who were previously exposed to short-time physical activity to others who are not exposed to it, but involved in different simple tasks. On average, we find that subjects exposed to physical activity exhibit more trust and pro-social behaviors than those who are not exposed. These effects are not temporary.
    Date: 2017–11
  10. By: Keser, Claudia; Müller, Stephan; Peterlé, Emmanuel; Rau, Holger A.
    Abstract: This paper experimentally tests the relation between subjects' competitiveness and bargaining behavior. Bargaining is investigated in a demand-ultimatum game, where the responder can request a share of the pie from the proposer. The results show that highly competitive proposers earn less, since they make lower offers, which are more often rejected. Similarly, highly competitive responders achieve lower payoffs, since they request excessive amounts which induces lower proposals. These findings establish a link between competitiveness and bargaining as suggested by social and evolutionary psychology. Thus, we identify one driver of the empirical heterogeneity of bargaining behavior and outcomes. From a management perspective our findings highlight that giving thought to employees' competitiveness before delegating them to participate in negotiations may pay off.
    Keywords: Bargaining,Competitiveness,Experiment
    JEL: C91 M54
    Date: 2018
  11. By: Clark, Derek J. (School of Business and Economics, University of Tromsø); Nilssen, Tore (Dept. of Economics, University of Oslo)
    Abstract: We consider an effort-maximizing principal distributing a prize fund over two consecutive all-pay auctions. The two contestants are doubly heterogeneous: one of them has a head start in the fi rst contest; and winning contest one gives an advantage in contest two that varies between players. We show that, with a large head start, the principal chooses a zero prize in contest two, i.e., runs a single contest. Otherwise, the laggard winning contest one may overturn the leaders head start, possibly inciting expected efforts equal to the prize value, avoiding the laggard giving up, and this way mitigating the Matthew effect.
    Keywords: Contest; All-pay auction; Head start; Catching up; Mathhew effect
    JEL: D72 D74
    Date: 2018–02–27
  12. By: Hardik Rajpal; Deepak Dhar
    Abstract: We discuss the strategy that rational agents can use to maximize their expected long-term payoff in the co-action minority game. We argue that the agents will try to get into a cyclic state, where each of the $(2N +1)$ agent wins exactly $N$ times in any continuous stretch of $(2N+1)$ days. We propose and analyse a strategy for reaching such a cyclic state quickly, when any direct communication between agents is not allowed, and only the publicly available common information is the record of total number of people choosing the first restaurant in the past. We determine exactly the average time required to reach the periodic state for this strategy. We show that it varies as $(N/\ln 2) [1 + \alpha \cos (2 \pi \log_2 N)$], for large $N$, where the amplitude $\alpha$ of the leading term in the log-periodic oscillations is found be $\frac{8 \pi^2}{(\ln 2)^2} \exp{(- 2 \pi^2/\ln 2)} \approx {\color{blue}7 \times 10^{-11}}$.
    Date: 2018–02
  13. By: Schlegel, J. C.
    Abstract: We study ex-ante priority respecting (ex-ante stable) lotteries in the context of object allocation under thick priorities. We show that ex-ante stability as a fairness condition is very demanding: Only few agent-object pairs have a positive probability of being matched in an ex-ante stable assignment. We interpret our result as an impossibility result. With ex-ante stability one cannot go much beyond randomly breaking ties and implementing a (deterministically) stable matching with respect to the broken ties.
    Keywords: Matching; School Choice; Lotteries; Ex-Ante Stability
    Date: 2017
  14. By: González, Stéphane; Laruelle, Annick; Solal, Philippe
    Abstract: In this article, the question is to select the “best” candidates within a set of candidates when voters cast approval-disapproval ternary ballots. That is, three options are offered to voters: casting a vote “in favor”, a “neutral” vote or a vote “against” each candidate. We first review desirable properties that a rule aggregating approval-disapproval ternary ballots should satisfy. We check whether the rules that have been proposed in the literature satisfy them. Then, we provide comparable axiomatizations of three rules: one is the lexicographical extension of the Approval rule for binary ballots; the second is the lexicographical extension of the Disapproval rule for binary ballots; and the third rule eliminates candidates with more opponents and fewer supporters than other candidates.
    Keywords: approval, disapproval, voting, compromise, condorcet, principle
    JEL: D71 D72
    Date: 2017–11–24
  15. By: Francesca Busetto; Giulio Codognato; Sayantan Ghosal; Ludovic A. Julien; Simone Tonin
    Abstract: We consider a bilateral oligopoly version of the Shapley window model with large traders, represented as atoms, and small traders, represented by an atomless part. For this model, we provide a general existence proof of a Cournot-Nash equilibrium that allows one of the two commodities to be held only by atoms. Then, we show, using a corollary proved by Shitovitz (1973), that a Cournot-Nash allocation is Pareto optimal if and only if it is a Walras allocation.
    Keywords: Shapley window model; Atoms; Atomless part; Cournot–Nash equilibrium; Optimality
    JEL: C72 D51
    Date: 2018
  16. By: Sigit Perdana; Rod Tyers
    Abstract: Global agreement to reduce carbon emissions has been weakened by slowing growth and burden-sharing conflicts. This paper examines strategic interaction amongst regions in the choice to implement carbon taxation. Benefits from climate change mitigation are constructed via a meta-analysis of existing studies that link carbon concentration with average surface temperature and region-specific measures of economic welfare. Implementation costs are then derived by modeling national and global economic performance. Multiplayer, normal form games with payoffs derived by netting costs from shared benefits are then constructed, revealing that the US and China are net gainers in net present value terms from unilateral implementation. Europe’s choice is marginal but sensitive to the temperature scenario. The dominant strategy for all other countries is to free ride. For the three large economies, there are net gains that are bolstered by universal adoption. In total, the compensatory side payments that would induce universal adoption are sufficient and affordable. The net gains to all regions do not begin to appear for at least two decades, rendering commitment to abatement politically difficult.
    Keywords: Climate change, Carbon taxation, Global dynamic general equilibrium analysis
    JEL: F47 Q34 Q54
    Date: 2018–02
  17. By: Kristoffer Arnsfelt Hansen; Rasmus Ibsen-Jensen; Abraham Neyman
    Abstract: The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage. Blackwell and Ferguson (1968) give an $\varepsilon$-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless. The present paper proves that there is such a strategy that is $\varepsilon$-optimal. In fact, we show that just two states of memory are sufficient.
    Date: 2018–02
  18. By: Hiroshi Kitamura; Noriaki Matsushima; Misato Sato
    Abstract: This study constructs a model of anticompetitive exclusive-offer competition between two existing upstream firms. Under exclusive-offer competition, the upstream firm's profit depends on the rival's exclusive offer. If the rival makes an exclusive offer acceptable for the downstream firm, the upstream firm is excluded unless it succeeds in exclusion. Consequently, the upper bound of exclusive offers becomes higher than when one of the upstream firms is a potential entrant that cannot make any exclusive offer. Thus, the exclusion of the existing upstream firm can be an equilibrium outcome even in the case where the potential entrant is never excluded.
    Date: 2018–03
  19. By: Elliott, M.; Golub, B.
    Abstract: Suppose agents can exert costly effort that creates nonrival, heterogeneous benefits for each other. At each possible outcome, a weighted, directed network describing marginal externalities is defined. We show that Pareto efficient outcomes are those at which the largest eigenvalue of the network is 1. An important set of efficient solutions - Lindahl outcomes - are characterized by contributions being proportional to agents' eigenvector centralities in the network. The outcomes we focus on are motivated by negotiations. We apply the results to identify who is essential for Pareto improvements, how to efficiently subdivide negotiations, and whom to optimally add to a team.
    Date: 2018–02–07
  20. By: Lefouili, Yassine; Pinho, Joana
    Abstract: This paper explores the incentives for, and the effects of, collusion in prices between two-sided platforms. We characterize the most profitable sustainable agreement when platforms collude on both sides of the market and when they collude on a single side of the market. Under two-sided collusion, prices on both sides are higher than competitive prices, implying that agents on both sides become worse off as compared to the competitive outcome. An increase in cross-group externalities makes two-sided collusion harder to sustain, and reduces the harm from collusion suffered by the agents on a given side as long as the collusive price on that side is lower than the monopoly price. When platforms collude on a single side of the market, the price on the collusive side is lower (higher) than the competitive price if the magnitude of the cross-group externalities exerted on that side is sufficiently large (small). As a result, one-sided collusion may benefit the agents on the collusive side and harm the agents on the competitive side.
    Keywords: Collusion; Two-sided markets; Cross-group externalities
    JEL: D43 L41
    Date: 2018–02
  21. By: Hackbarth, Dirk; Taub, Bart
    Abstract: We study anti-competitive mergers in a dynamic model with noisy collusion. At each instant, firms either privately choose output levels or merge, which trades off benefits of avoiding price wars against the costs of merging. There are three results. First, mergers are optimal when collusion fails (i.e., firms sufficiently deviate from a collusive regime). Second, long periods of collusion are likely, because colluding is dynamically stable. Therefore, mergers are rare. Third, mergers (and, in particular, lower merger costs) decrease pre-merger collusion, as punishments by price wars are weakened. Thus, although anti-competitive mergers harm competition ex-post, barriers and costs of merging due to regulation should be reduced to promote competition ex-ante.
    Keywords: Competition; Horizontal mergers; imperfect information; Industry Structure; market power
    JEL: D43 G34 L12 L13
    Date: 2018–02

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