nep-gth New Economics Papers
on Game Theory
Issue of 2018‒02‒19
25 papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Sharing the revenues from broadcasting sport events By Gustavo Bergantiños; Juan D. Moreno-Ternero
  2. Incentivizing Efficiency in Local Public Good Games and Applications to the Quantification of Personal Data in Networks By Michela Chessa; Patrick Loiseau
  3. Dynamic Communication with Biased Senders By Margaria, Chiara; Smolin, Alex
  4. Group behaviour in tacit coordination games with focal points: An experimental investigation By Stefania Sitzia; Jiwei Zheng
  5. GAMES WITH IDENTICAL SHAPLEY VALUES By Sylvain Béal; MIHAI MANEA; Eric Rémila; Phillippe Solal
  6. Knowledge and Acceptance of Core Payoffs: An Epistemic Foundation for Cooperative Game Theory By Shuige Liu
  7. Sion's minimax theorem and Nash equilibrium of symmetric multi-person zero-sum game By Satoh, Atsuhiro; Tanaka, Yasuhito
  8. An exploratory study of how sleep restriction impacts choice in two classic normal form games. By David L. Dickinson
  9. Strategic Default in Financial Networks By Nizar Allouch; Maya Jalloul
  10. A Note on Stable Cartels By Mao, Liang
  11. Guilt and participation By Amrish Patel; Alec Smith
  12. Robust policy schemes for R&D games with asymmetric information By Anton Bondarev
  13. Voluntary disclosure in unfair contests By Christian Ewerhart; Julia Grünseis
  14. Dynamic Evaluation Design By Smolin, Alex
  15. Disclosure and Pricing of Attributes By Smolin, Alex
  16. What breaks the chain of unkindness: emotional closure or signaling? By Wendelin Schnedler; Nina Lucia Stephan
  17. Uninvadable social behaviors and preferences in group-structured populations By Alger, Ingela; Lehmann, Laurent; Weibull, Jörgen W.
  18. Optimization of Fire Sales and Borrowing in Systemic Risk By Maxim Bichuch; Zachary Feinstein
  19. Search and Information Costs By Miao, Chun-Hui
  20. Bayesian persuasion with heterogeneous priors By Alonso, Ricardo; Câmara, Odilon
  21. Market Structure in Bitcoin Mining By June Ma; Joshua S. Gans; Rabee Tourky
  22. Assigning an unpleasant task without payment By Susanne Goldlücke; Thomas Tröger
  23. Number of bidders and the winner’s curse By Ronald Peeters; Anastas P. Tenev
  24. Demand response as a common pool resource game: Nudges versus prices By Buckley, P.; Llerena, D.
  25. Biases in Beliefs: Experimental Evidence By Dominik Bauer; Irenaeus Wolff

  1. By: Gustavo Bergantiños (ECOSOT, Universidade de Vigo); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide;)
    Abstract: We study the problem of sharing the revenue from broadcasting sport events, among participating players. We provide direct, axiomatic and game-theoretical foundations for two focal rules: the equal-split rule and concede-and-divide. The former allocates the revenues generated from broadcasting each game equally among the participating players in the game. The latter concedes players in each game the revenues generated by their respective fans and divides equally the residual. We also provide an application studying the case of sharing the revenue from broadcasting games in La Liga, the Spanish Football League. We show that hybrid schemes, combining our rules with lower bounds and performance measures, yield close outcomes to the current allocation being implemented by the Spanish National Professional Football League Association.
    Keywords: resource allocation, broadcasting, sport events, concede-and-divide, Shapley value
    JEL: D63 C71
    Date: 2018–02
  2. By: Michela Chessa (Université Côte d'Azur, France; GREDEG CNRS); Patrick Loiseau (Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG; Max Planck Institute for Software Systems (MPI-SWS))
    Abstract: A well established principle arms that the privacy of individuals is respected whenever they are entitled to control the dissemination of their personal data and they are fairly compensated. From this perspective, quantifying the value of personal data is a crucial task in the Internet economics. This task is dicult, however, as the privacy attitude of the users is often characterized by a contradictory behavior, known as the privacy paradox, in which they declare to be sensitive to privacy losses but also often release large amounts of data to enjoy free services. In this paper, we model this trade-off as a local public good game and propose some quantifications of the users' personal data depending on their position in the social network, based on enhancing an efficient solution of the local public good model. In a first part, we present some non-cooperative approaches, based on an internalization of the local externalities. In a second part, we extend the model to a cooperative game and we apply some well-known solutions from cooperative game theory to suggest fair ways to compensate the users and to perform a network analysis.
    Keywords: Personal Data, Social Network, Local Public Good Game, Cooperative Game Theory, Core, Shapley value
    JEL: C71 C72 D62 D85 H41
    Date: 2018–02
  3. By: Margaria, Chiara; Smolin, Alex
    Abstract: We study dynamic games in which senders with state-independent payoffs communicate to a single receiver. Senders’ private information evolves according to an aperiodic and irreducible Markov chain. We prove an analog of a folk theorem—that any feasible and individually rational payoff can be approximated in a perfect Bayesian equilibrium if players are sufficiently patient. In particular, there are equilibria in which the receiver makes perfectly informed decisions in almost every period, even if no informative communication can be sustained in the stage game. We conclude that repeated interaction can overcome strategic limits of communication.
    Keywords: Bayesian games, repeated games, communication, folk theorem
    JEL: C72 C73 D82 D83
    Date: 2017–10
  4. By: Stefania Sitzia (University of East Anglia); Jiwei Zheng (Universtiy of East Anglia)
    Abstract: This paper reports an experimental investigation of Schelling's theory of focal points that compares group and individual behaviour. We find that when players' interests are perfectly aligned, groups choose more often the label salient option and achieve higher coordination success than individuals. However, in games with conflict of interest, groups do not always perform better than individuals, especially when the degree of conflict is substantial. We also find that groups outperform individuals in games in which identifying the solution to the coordination problem requires some level of cognitive sophistication (i.e. trade-off games). Finally, players that successfully identify the solution to these games achieve also greater coordination rates in games with a low degree of conflict than other players. This result raises questions of whether finding the focal point is more a matter of logic rather than imagination as instead Schelling argued.
    Keywords: groups, coordination, label cues, cognition
    JEL: C72 C78 C91 C92
    Date: 2018–01–30
  5. By: Sylvain Béal (Université de Bourgogne Franche-Comté, CRESE); MIHAI MANEA; Eric Rémila (Université de Saint-Etienne, Gate); Phillippe Solal (Université de Saint-Etienne, Gate)
    Abstract: We discuss several sets of cooperative games in which the Shapley value assigns zero payo s to all players. Each set spans the kernel of the Shapley value and leads to a different characterization of games with identical Shapley values. The special games we identify deliver intuitive axiomatizations of the Shapley value. We explain how each basis of the kernel of the Shapley value can be augmented to construct a basis of the space of all games.
    Keywords: Shapley value, kernel, axiomatization, factious oligarchies, paper tigers
    Date: 2018–02
  6. By: Shuige Liu
    Abstract: We provide an epistemic foundation for the core of a cooperative game by proof theory. Given a cooperative game, we first transform each payoff vector into a decision problem (accept or reject) for each player. Then we use a modified KD-system in epistemic logic to describe a player's belief/knowledge, decision-making criterion, and reasoning process. Especially, we define C-acceptability to capture the criterion for a core payoff vector. Within this syntactical framework, we characterize the core of a cooperative game in terms of each player's knowledge. Based on this result, we discuss epistemic inconsistency behind Debreu-Scarf Theorem.
    Date: 2018–02
  7. By: Satoh, Atsuhiro; Tanaka, Yasuhito
    Abstract: About a symmetric multi-person zero-sum game we will show the following results. 1. Sion's minimax theorem plus the coincidence of the maximin strategy and the minimax strategy are proved by the existence of a symmetric Nash equilibrium. 2. The existence of a symmetric Nash equilibrium is proved by Sion's minimax theorem plus the coincidence of the maximin strategy and the minimax strategy. Thus, they are equivalent. If a zero-sum game is asymmetric, maximin strategies and minimax strategies of players do not correspond to Nash equilibrium strategies. If it is symmetric, the maximin strategies and the minimax strategies constitute a Nash equilibrium. However, with only the minimax theorem there may exist an asymmetric equilibrium in a symmetric multi-person zero-sum game.
    Keywords: multi-person zero-sum game, Nash equilibrium,Sion's minimax theorem
    JEL: C72
    Date: 2018–02–13
  8. By: David L. Dickinson
    Abstract: We experimentally manipulate sleep levels to examine the impact of sleepiness on strategic oneshot interactions. Where multiple Nash equilibria exist (the Battle-of-the-Sexes game), sleepy subjects play closer to the mixed strategy prediction than do well-rested subjects. When there is a unique equilibrium in mixed strategies (the Penalty Kick game), strategy play of sleepy subject shows indications of reinforcement play. Sleepiness may, at least in some games, promote use of simple heuristics that focus on previous outcomes even when interactions are one-shot. Key Words: Sleep deprivation, game theory, heuristics, experiments
    JEL: C92 D91 C72
    Date: 2018
  9. By: Nizar Allouch; Maya Jalloul
    Abstract: This paper investigates a model of strategic interactions in financial networks, where the decision by one agent on whether or not to default impacts the incentives of other agents to escape default. Agents’ payoffs are determined by the clearing mechanism introduced in the seminal contribution of Eisenberg and Noe (2001). We first show the existence of a Nash equilibrium of this default game. Next, we develop an algorithm to find all Nash equilibria that relies on the financial network structure. Finally, we explore some policy implications to achieve efficient coordination.
    Keywords: systemic risk; default; financial networks; coordination games; central clearing counterparty; financial regulation
    JEL: C72 D53 D85 G21 G28 G33
    Date: 2017–12
  10. By: Mao, Liang
    Abstract: In non-cooperative open membership cartel formation games, it is usually assumed that cartel members will maximize their joint payoffs. Through an example, this note shows that this assumption is problematic, because it imposes some unnecessary restrictions on cartel members' actions. We recommend that the cartel agreement should be endogenously determined in future studies.
    Keywords: cartel formation, stable cartel, self-enforcing agreement
    JEL: C79 H41
    Date: 2017–11–14
  11. By: Amrish Patel (University of East Anglia); Alec Smith (Virginia Tech University)
    Abstract: How does guilt affect participation in providing public goods? We characterise and analyse completely mixed symmetric equilibria (CMSE) in participation games where players are guilt averse. We find that relative to material preferences, guilt aversion can: facilitate the existence of CMSE; increase or decrease participation; and imply that group size has a non-monotonic effect on participation. Using our equilibrium characterisation we also re-analyse experimental data on participation games and find a low, but positive, guilt sensitivity parameter.
    Keywords: participation, threshold public good, volunteer's dilemma, psychological games, guilt aversion
    JEL: C72 H41
    Date: 2018–01–30
  12. By: Anton Bondarev (University of Basel)
    Abstract: We consider an abstract setting of the differential r&d game, where participating firms are allowed for strategic behavior. We assume the information asymmetry across those firms and the government, which seeks to support newer technologies in a socially optimal manner. We develop a general theory of robust subsidies under such one-sided uncertainty and establish results on relative optimality, duration and size of different policy tools available to the government. It turns out that there might exist multiple sets of second-best robust policies, but there always exist a naturally induced ordering across such sets, implying the optimal choice of a policy exists for the government under different uncertainty levels.
    Keywords: technology lock-in, technological change, strategic interaction, uncertainty, robust policy sets, uncertainty thresholds, robust welfare improving policy, axiom of choice
    JEL: C02 C61 O31 O38
    Date: 2018
  13. By: Christian Ewerhart; Julia Grünseis
    Abstract: This paper studies incentives for the interim voluntary disclosure of verifiable information in probabilistic all-pay contests. Considered are unfair contests, i.e., contests in which, subject to activity conditions, one player (the favorite) is interim always more likely to win than the other player (the underdog). A condition is identified that ensures that a given contest is unfair regardless of disclosure decisions. Under this condition, full revelation is the unique perfect Bayesian equilibrium outcome of the contest with pre-play communication. This is so because the weakest type of the underdog will try to moderate the favorite, while the strongest type of the favorite will try to discourage the underdog - so that the contest unravels. We also show that self-disclosure may, with positive probability, provoke unintended reactions, i.e., "dominant" or "defiant" behavior. Moreover, while individually rational for the marginal type, the unraveling may be strictly Pareto inferior from an ex-ante perspective. Our main conclusion is just the opposite of the corresponding finding for the deterministic all-pay auction. The proofs employ lattice-theoretic methods and an improved version of Jensen's inequality.
    Keywords: Unfair contests, incomplete information, self-disclosure, unraveling, strategic complements and substitutes, dominance and defiance
    JEL: C72 D74 D82 J71
    Date: 2018–02
  14. By: Smolin, Alex
    Abstract: A principal owns a firm, hires an agent of uncertain productivity, and designs a dynamic policy for evaluating his performance. The agent observes ongoing evaluations and decides when to quit. While not quitting, the agent is paid a wage proportional to his perceived productivity; the principal claims the residual performance. After quitting, the agent secures a fixed safe payoff. I show that equilibrium evaluation policies are Pareto efficient and leave no rents to the agent. In a minimally informative equilibrium, for a broad class of performance technologies, the agent’s wage deterministically grows with tenure.
    Keywords: evaluation, information design, career concerns, bandit experimentation, downward wage rigidity, up-or-out
    JEL: C72 D82 D83 M52
    Date: 2017–10
  15. By: Smolin, Alex
    Abstract: A monopolist seller owns an object that has several attributes. A buyer is privately informed about his tastes and uncertain about the attributes. The seller can disclose attribute information to the buyer in a form of a statistical experiment. The seller offers a menu of call options varying in upfront payments, experiments, and strike prices. I study revenue-maximizing menus and show that optimal experiments belong to a simple class of linear disclosures. I fully characterize an optimal menu for a class of single-minded buyers. Surprisingly, the menu is nondiscriminatory and can be implemented by a single partial disclosure followed by a posted price.
    Keywords: Attributes, Information Design, Mechanism Design, Private Disclosure, Call Options, Multidimensional Screening, Demand Transformation
    JEL: D42 D82 D83
    Date: 2017–10
  16. By: Wendelin Schnedler (University of Paderborn); Nina Lucia Stephan (University of Paderborn)
    Abstract: Previous experimental studies show that subjects who receive little in a dictator game, pass on less to a third person when they are dictators themselves (they reciprocate negatively to a third party). However, when they can write a letter to their dictator, subjects are less likely to pass on the unkindness. There are two potential explanations for this phenomenon: First, writing the letter may help to emotionally ‘close the case’ (closure explanation). Second, the opportunity to write a letter is a sign that it is not ‘ok’ to imitate the previous dictator (signal explanation). The present study examines with an experiment which explanation is more suitable.\\ The novelty in our design is a domain shift, making imitation impossible: The first subject does not decide on how to split a pot of money but can instead treat the second subject unkindly by assigning her to an annoying instead of a funny task. We find that letter writing nevertheless increases the average amount passed on in the subsequent dictator game. Thus, the closure explanation is perhaps more suitable. There is, however, one caveat: while writing the letter may make people emotionally ‘close the case’, this is not reflected in how happy people rate themselves.
    Keywords: experimental economics, chain of unkindness, imitation, emotional closure, cooling down
    JEL: D91 C91 D03
    Date: 2018–01
  17. By: Alger, Ingela; Lehmann, Laurent; Weibull, Jörgen W.
    Abstract: Humans have evolved in populations structured in groups that extended beyond the nuclear family. Individuals interacted with each other within these groups and there was limited migration and sometimes conáicts between these groups. Suppose that during this evolution, individuals transmitted their behaviors or preferences to their (genetic or cultural) o§spring, and that material outcomes resulting from the interaction determined which parents were more successful than others in producing (genetic or cultural) o§spring. Should one then expect pure material self-interest to prevail? Some degree of altruism, spite, inequity aversion or morality? By building on established models in population biology we analyze the role that di§erent aspects of population structureó such as group size, migration rates, probability of group conáicts, cultural loyalty towards parentsó play in shaping behaviors and preferences which, once established, cannot be displaced by any other preference. In particular, we establish that uninvadable preferences under limited migration between groups will consist of a materially self-interested, a moral, and an other-regarding component, and we show how the strength of each component depends on population structure.
    Keywords: Strategic interactions; Preference evolution; Evolution by natural selection; Cultural transmission; Pro-sociality; Altruism; Morality; Spite
    JEL: A12 A13 B52 C73 D01 D63 D64 D91
    Date: 2018–02
  18. By: Maxim Bichuch; Zachary Feinstein
    Abstract: This paper provides a framework for modeling financial contagion in a network subject to fire sales and price impacts, but allowing for firms to borrow to cover their shortfall as well. We consider both uncollateralized and collateralized loans. The main results of this work are providing sufficient conditions for existence and uniqueness of the clearing solutions (i.e., payments, liquidations, and borrowing); in such a setting any clearing solution is the Nash equilibrium of an aggregation game.
    Date: 2018–02
  19. By: Miao, Chun-Hui
    Abstract: In many markets, consumers obtain price quotes before making purchases. In this paper, I consider a fixed-sample size model of search for price quotes when sellers must spend resources to learn the true cost of providing goods/services. I find that (1) even with ex ante identical and rational consumers and sellers, there is price dispersion in the equilibrium; (2) the expected equilibrium price can decrease with the search cost of consumers; (3) consumers may engage in excessive search that is detrimental to their own welfare; (4) a decline in the search cost can leave consumers worse off, due to their lack of commitment.
    Keywords: Price dispersion, Precontract cost, Search cost, Sealed-bid Auction.
    JEL: D4 D40 L0
    Date: 2017–06–30
  20. By: Alonso, Ricardo; Câmara, Odilon
    Abstract: In a world in which rational individuals may hold different prior beliefs, a sender can influence the behavior of a receiver by controlling the informativeness of an experiment (public signal). We characterize the set of distributions of posterior beliefs that can be induced by an experiment, and provide necessary and sufficient conditions for a sender to benefit from persuasion. We then provide sufficient conditions for the sender to benefit from persuasion for almost every pair of prior beliefs, even when there is no value of persuasion under a common prior. Our main condition is that the receiver's action depends on his beliefs only through his expectation of some random variable.
    Keywords: persuasion; strategic experimentation; heterogeneous priors
    JEL: D72 D83 M31
    Date: 2016–09–01
  21. By: June Ma; Joshua S. Gans; Rabee Tourky
    Abstract: We analyze the Bitcoin protocol for electronic peer-to-peer payments and the operations that support the “blockchain” that underpins it. It is shown that that protocol maps formally into a dynamic game that is an extension of standard models of R&D racing. The model provides a technical foundation for any economic analysis of ‘proof of work’ protocols. Using the model, we demonstrate that free entry is solely responsible for determining resource usage by the system for a given reward to mining. The endogenous level of computational difficulty built into the Bitcoin protocol does not mitigate this usage and serves only to determine the time taken to process transactions. Regulating market structure will mitigate resource use highlighting the importance of identifying the benefits of competition for the operation of the blockchain.
    JEL: E42 L1
    Date: 2018–01
  22. By: Susanne Goldlücke; Thomas Tröger
    Abstract: How should a group of people decide to allocate a task that has to be done but is not adequately rewarded? This paper finds an optimal mechanism for the private provision of a public service in an environment without monetary transfers. All members of the group have the same cost of providing the service, but some individuals are better suited for the task than others. The optimal mechanism is a threshold rule that assigns the task randomly among volunteers if enough volunteers come forward, and otherwise assigns the task among the non-volunteers.
    Keywords: Volunteering; public good provision; mechanism design
    JEL: D82 D71 D62 H41
    Date: 2018–02
  23. By: Ronald Peeters (Department of Economics, University of Otago, New Zealand); Anastas P. Tenev (Department of Economics, Maastricht University)
    Abstract: Within an affiliated value auction setting, we study the relationship between the number of bidders and the winner’s curse in terms of its occurrence and its expected harm. From a design perspective, we find that both the number of bidders and the level of affiliation are instrumental when choosing an auction format and whether to encourage or discourage bidder participation.
    Keywords: Winner’s curse; number of bidders; affiliated value auctions
    JEL: D44 D82 H57
    Date: 2018–01
  24. By: Buckley, P.; Llerena, D.
    Abstract: The aim of demand response is to make energy consumption more flexible during peak periods. Using a contextualised CPR framework, we study energy consumption choices. Subjects decide the consumption level of five activities during 10 periods. The total consumption of these activities is the CPR contribution, and payoffs depend on own consumption and the amount consumed by the group. In the nudge treatment, subjects are nudged towards the socially optimal level of consumption using injunctive norms. The average consumption observed in the nudge treatment is used to calculate the price implemented in the price treatment. The objective is to quantify the nudge via an equivalent price. The main hypotheses are: consumption choices will be lower in the treatment groups compared to the control groups; when the price level is fixed according to the nudge result, consumption choices in the price treatment will be equivalent to those in the nudge treatment. Across all 10 periods, consumption is significantly lower in the nudge treatment, and higher for control groups. In the price treatment, consumption remains between the two at or slightly above the target. We conclude that the nudge treatment performs as well as an equivalent price without the implied loss of welfare. When comparing decisions under the nudge and price treatments to the control groups, the consumption decisions are significantly different from period 2 for the nudge and, consistently different from period 7 for the price. We conclude that the nudge is understood and integrated into subjects' decision making quicker than an equivalent price.
    JEL: C91 C92 D62 D91 H21
    Date: 2018
  25. By: Dominik Bauer; Irenaeus Wolff
    Abstract: Many papers have reported behavioral biases in belief formation that come on top of standard game-theoretic reasoning. We show that the processes involved depend on the way participants reason about their beliefs. When they think about what everybody else or another ‘unspeci€fied’ individual is doing, they exhibit a consensus bias (believing that others are similar to themselves). In contrast, when they think about what their situation-speci€fic counterpart is doing, they show ex-post rationalization, under which the reported belief is €‹fitted to the action and not vice versa. Our €findings suggest that there may not be an ‘innocent’ belief-elicitation method that yields unbiased beliefs. However, if we ‘debias’ the reported beliefs using our estimates of the di‚fferent e‚ffects, we €find no more treatment e‚ffect of how we ask for the belief. ‘The ‘debiasing’ exercise shows that not accounting for the biases will typically bias estimates of game-theoretic thinking upwards.
    Keywords: Belief Elicitation, Belief Formation, Belief-Action Consistency, Framing E‚ffects, Projection, Consensus E‚ffect, Wishful ‘Thinking, Hindsight Bias, Ex-Post Rationalization
    Date: 2018

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