nep-gth New Economics Papers
on Game Theory
Issue of 2021‒03‒22
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Making the most of potential: potential games and genotypic convergence By Omer Edhan; Ziv Hellman; Ilan Nehama
  2. Disentangle the Florentine Families Network by the Pre-Kernel By Meinhardt, Holger Ingmar
  3. The grand dividends value By Besner, Manfred
  4. Balanced Externalities and the Proportional Allocation of Nonseparable Contributions By Rene van den Brink; Youngsub Chun; Yukihiko Funaki; Zhengxing Zou
  5. Mean Field Contest with Singularity By Marcel Nutz; Yuchong Zhang
  6. Preferences, Uncertainty, and Biases in Land Division: A Bargaining Experiment in the Field By Gafaro, M; Mantilla, C
  7. Approachability with Discounting By Carmona, G.; Sabourian, H.
  8. Unbeatable strategies By Rabah Amir; Igor V. Evstigneev; Valeriya Potapova
  9. Oligopoly model with interdependent preferences: existence and uniqueness of Nash equilibrium By Marco F. Boretto; Fausto Cavalli; Ahmad Naimzada
  10. Robust equilibrium strategies in a defined benefit pension plan game By Guohui Guan; Jiaqi Hu; Zongxia Liang
  11. Group identification and giving: in-group love, out-group hate and their crowding out By Shaun P. Hargreaves Heap; Eugenio Levi; Abhijit Ramalingam
  12. Optimal auctions with signaling bidders By Bos, Olivier; Pollrich, Martin
  13. Inconsistent weighting in weighted voting games By Sylvain Béal; Marc Deschamps; Mostapha Diss
  14. Provision of noxious facilities using a market-like mechanism: A simple implementation in the lab By Alberti, F; Mantilla, C
  15. Portfolio risk allocation through Shapley value By Patrick S. Hagan; Andrew Lesniewski; Georgios E. Skoufis; Diana E. Woodward
  16. Phase Transitions in Kyle's Model with Market Maker Profit Incentives By Charles-Albert Lehalle; Eyal Neuman; Segev Shlomov
  17. A Survey on Nonstrategic Models of Opinion Dynamics By Michel Grabisch; Agnieszka Rusinowska
  18. Confrontation Costs in Negotiations: Bargaining Under the Veil of a Screen By Andrés Gago
  19. Optimal Delegation and Information Transmission Under Limited Awareness By Sarah Auster; Nicola Pavoni
  20. Competition in Signaling By Federico Vaccari
  21. Personal and social norms in a multilevel public goods experiment By Marco Catola; Simone D'Alessandro; Pietro Guarnieri; Veronica Pizziol

  1. By: Omer Edhan; Ziv Hellman; Ilan Nehama
    Date: 2020
  2. By: Meinhardt, Holger Ingmar
    Abstract: For different model settings we conduct power analyses on the Florentine families network of the 15th century while referring to the most popular power indices like the Shapley-Shubik or Banzhaf value as well as to the pre-nucleolus and pre-kernel. In order to assess their capacity to identify the main protagonists that correspond with the chronicles, we inspect of how the power distributions are spread around the mean. Distributions that are clustered to close around the mean cannot identify outstanding positions. In this respect, they failed to provide a scenario that corresponds with the annals. As it turns out, the pre-kernel solution – as a solution concept designed for studying bargaining situations – retrieves the most accurate image for the examined network structures. Last but not least, we discovered two new non-homogeneous weighted majority games with a disconnected pre-kernel.
    Keywords: Transferable Utility Game, (Non-)Homogeneous Game, Disconnected Pre-Kernel, Convex Analysis, Fenchel-Moreau Conjugation, Pre-Nucleolus, Shapley-Shubik Index, Banzhaf Value, Deegan-Packel Index, Johnston Index, Public Good Index.
    JEL: C71
    Date: 2021–03–06
  3. By: Besner, Manfred
    Abstract: We introduce a new value for games with transferable utility, called grand dividends value. In the payoff calculation, the grand dividends value takes into account the worths of all subcoalitions of a player set. The concept of grand dividends, representing the surplus (which can also be non-positive) of the worth of the grand coalition over the worths of all coalitions that lack one player of the player set, is the initial point here. The grand dividends value satisfies many properties that we know from the Shapley value. Along with new axioms that have a similar correspondence to axioms that are also satisfied by the Shapley value, axiomatizations arise that have an analogous equivalent for the Shapley value, including the classics of Shapley and Young.
    Keywords: Cooperative game; (Harsanyi/Grand) Dividends; Shapley value; Grand dividends value
    JEL: C7 C71
    Date: 2021–03–16
  4. By: Rene van den Brink (Vrije Universiteit Amsterdam); Youngsub Chun (Seoul National University); Yukihiko Funaki (Waseda University); Zhengxing Zou (Beijing Jiaotong University)
    Abstract: In this paper, we study the implications of extending the balanced cost reduction property from queueing problems to general games. As a direct translation of the balanced cost reduction property, the axiom of balanced externalities for solutions of games, requires that the payoff of any player is equal to the total externality she inflicts on the other players with her presence. We show that this axiom and efficiency together characterize the Shapley value for 2-additive games. However, extending this axiom in a straightfoward way to general games is incompatible with efficiency. Keeping as close as possible to the idea behind balanced externalities, we weaken this axiom by requiring that every player's payoff is the same fraction of its total externality inflicted on the other players. This weakening, which we call weak balanced externalities, turns out to be compatible with efficiency. More specifically, the unique efficient solution that satisfies this weaker property is the proportional allocation of nonseparable contribution (PANSC) value, which allocates the total worth proportional to the separable costs of the players. We also provide characterizations of the PANSC value using a reduced game consistency axiom.
    Keywords: Cooperative game, balanced externalities, proportional allocation of nonseparable contributions, consistency
    JEL: C71
    Date: 2021–03–18
  5. By: Marcel Nutz; Yuchong Zhang
    Abstract: We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean field equilibrium and it is shown to be the limit of associated $n$-player games. Conversely, the mean field strategy induces $n$-player $\varepsilon$-Nash equilibria for any continuous reward function -- but not for discontinuous ones. In a second part, we study the problem of a principal who can choose how to distribute a reward budget over the ranks and aims to maximize the performance of the median player. The optimal reward design (contract) is found in closed form, complementing the merely partial results available in the $n$-player case. We then analyze the quality of the mean field design when used as a proxy for the optimizer in the $n$-player game. Surprisingly, the quality deteriorates dramatically as $n$ grows. We explain this with an asymptotic singularity in the induced $n$-player equilibrium distributions.
    Date: 2021–03
  6. By: Gafaro, M; Mantilla, C
    Abstract: Divisions of rural land in developing countries reduce the possibilities of farmers to profit from agricultural returns to scale. We design and conduct a framed bargaining experiment to study whether land overvaluation (due to affective reasons) and uncertainty in land values are drivers for land division. In our bargaining game, two players with different agricultural productivity jointly inherit a land plot and individually inherit some tokens they can use to agree on a land allocation. The possible set of land allocations and the spread of land returns vary across treatment arms in the game. We conduct this experiment with 256 participants in eight rural municipalities of the Northeast of Colombia. We find that when players are allowed to divide the land plot, 75% of the bargaining interactions yield the most egalitarian, but less efficient, land allocations. Based on the predictions of a Nash bargaining model and the observations from a sample of 120 college students, we rule out land overvaluation as a driver for land divisions in the context of our game. We also find that uncertainty in land yields reduces the efficiency of land allocations when we do not allow land divisions, by increasing the likelihood of the least productive player keeping the entire land plot. Our results are consistent with a bounded rationality rule in which subjects incorporate a behavioral response to uncertainty by first bargaining over land, which is a certain outcome, and then bargaining over a token transfer.
    Keywords: land division; Nash bargaining; affective value of land; nonuse value
    JEL: C78 C90 O13 Q15
    Date: 2019–09–03
  7. By: Carmona, G.; Sabourian, H.
    Abstract: We establish a version of Blackwell’s (1956) approachability result with discounting. Our main result shows that, for convex sets, our notion of approachability with discounting is equivalent to Blackwell’s (1956) approachability. Our proofs are based on a concentration result for probability measures and on the minmax theorem for two-person, zero-sum games.
    Keywords: Approachability, Repeated Games
    JEL: C72 C73 C79
    Date: 2021–03–11
  8. By: Rabah Amir; Igor V. Evstigneev; Valeriya Potapova
    Date: 2021
  9. By: Marco F. Boretto; Fausto Cavalli; Ahmad Naimzada
    Abstract: We propose a model to describe and study the effect of social interdependent preferences in a Cournot oligopoly based on a game in which the utility functions of firms depend on a combination of weighted profits of their competitors. If social interaction is neglected, the model reduces to the classic Cournot game, diverting from it as the role of social interaction becomes more and more relevant. Several synthetic measures are proposed to summarize the overall behavior of the agents and some configurations characterized by particular interactional structures are presented. Finally, the study of the well-posedness of the proposed framework is investigated, in terms of the existence and uniqueness of Nash equilibria. To this end, we generalize the conditions under which the existence and/or uniqueness of Nash equilibrium in classic game is guaranteed for particular Cournotian oligopoly models without interdependent preferences. In particular, we focus on two families of oligopolies, respectively consisting of "concave" oligopolies and oligopolies with isoelastic demand function.
    Keywords: Cournot Game, Preference interdependence, Network, Nash Equilibrium, existence and uniqueness
    JEL: D43 C62 C70
    Date: 2021–03
  10. By: Guohui Guan; Jiaqi Hu; Zongxia Liang
    Abstract: This paper investigates the robust {non-zero-sum} games in an aggregated {overfunded} defined benefit (abbr. DB) pension plan. The sponsoring firm is concerned with the investment performance of the fund surplus while the participants act as a union to claim a share of the fund surplus. The financial market consists of one risk-free asset and $n$ risky assets. The firm and the union both are ambiguous about the financial market and care about the robust strategies under the worst case scenario. {The union's objective is to maximize the expected discounted utility of the additional benefits, the firm's two different objectives are to maximizing the expected discounted utility of the fund surplus and the probability of the fund surplus reaching an upper level before hitting a lower level in the worst case scenario.} We formulate the related two robust non-zero-sum games for the firm and the union. Explicit forms and optimality of the solutions are shown by stochastic dynamic programming method. In the end of this paper, numerical results are illustrated to depict the economic behaviours of the robust equilibrium strategies in these two different games.
    Date: 2021–03
  11. By: Shaun P. Hargreaves Heap (Department of Political Economy, King’s College London); Eugenio Levi (Department of Public Economics, Masaryk University); Abhijit Ramalingam (Department of Economics, Walker College of Business, Appalachian State University)
    Abstract: Using a dictator game experiment, we examine whether the introduction of group identities affects giving. Group identities can activate feelings of in-group love and out-group hate to create an in-group bias. In addition, group identities may spawn social sanctions that are designed to reinforce this in-group bias. We find that the aggregate effect on giving of group identities alone tends to be positive but depends on the relative size of two sub-sets of the subject pool: those who exhibit an in-group bias and those who do not. With the latter, the introduction of group identities has no effect on giving. With the former, the in-group bias arises from both in-group love and out-group hate and with interactions skewed towards own group members, in-group love will dominate to produce an increase in gifts. Sanctions too depend for their aggregate effect on the relative size of these two sub-sets in the population, but in the opposite way. This is because in-group biased preferences are crowded-in by the sanctions among the hitherto equal givers and in-group biased preferences are crowded-out among those who would otherwise exhibit the in-group bias.
    Keywords: dictator game, in-group love, out-group hate, crowding-out
    JEL: C72 C91 D31 D63 D91 J70 Z18
    Date: 2021–03
  12. By: Bos, Olivier; Pollrich, Martin
    Abstract: We study optimal auctions in a symmetric private values setting, where bidders' care about winning the object and a receiver's inference about their type. We reestablish revenue equivalence when bidders' signaling concerns are linear, and the auction makes participation observable via an entry fee. With convex signaling concerns, optimal auctions are fully transparent: every standard auction, which reveals all bids yields maximal revenue. With concave signaling concerns there is no general revenue ranking. We highlight a trade-off between maximizing revenue derived from signaling, and extracting information from bidders. Our methodology combines tools from mechanism design with tools from Bayesian persuasion.
    Keywords: optimal auctions,revenue equivalence,Bayesian persuasion,information design
    JEL: D44 D82
    Date: 2020
  13. By: Sylvain Béal (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France); Marc Deschamps (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France); Mostapha Diss (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France)
    Abstract: In a weighted voting game, each voter has a given weight and a coalition of voters is successful if the sum of its weights exceeds a given quota. Such voting systems translate the idea that voters are not all equal by assigning them different weights. In such a situation, two voters are symmetric in a game if interchanging the two voters leaves the outcome of the game unchanged. Two voters with the same weight are naturally symmetric in every weighted voting game, but the converse statement is not necessarily true. We call this latter type of scenario inconsistent weighting. We investigate the conditions that give rise to such a phenomenon within the class of weighted voting games. We also study how the choice of the quota and the total weight can affect the probability of observing inconsistent weighting. Finally, we investigate various applications where inconsistent weighting is observed.
    Keywords: Weighted voting games, symmetric voters, inconsistent weighting, probability.
    JEL: C7 D7
    Date: 2021–03
  14. By: Alberti, F; Mantilla, C
    Abstract: We study the provision of a public project that globally behaves as a public good but locally behaves as a private bad. This scenario imposes two problems: (i) finding a compensation that makes the project acceptable for the pre-determined host, and (ii) securing the budget to pay for the project and the required compensation. We use a market-like mechanism with two useful properties for this scenario: players can either contribute or request subsidies to fund the public project, and players have veto power over the desired project quantity. In our game, two players benefit from a waste incinerator facility, whereas the third group member, the host, is harmed if the facility is too large. We analyze the efficiency and the redistributive potential of this mechanism, with and without communication, among group members. We find that the probability of positive provision did not differ with and without communication. However, average provided quantities with respect to the efficient quantity increased from 54% to 81% with communication. We also find that contributions fell below the Lindahl taxes, allowing the players who benefit from a larger facility to accrue most of the efficiency gains. The latter result is consistent with the infrequent evidence of veto threats as a bargaining strategy.
    Keywords: lab experiment; NIMBY; LULU; public goods;
    JEL: C92 H4 Q58
    Date: 2020–03–20
  15. By: Patrick S. Hagan; Andrew Lesniewski; Georgios E. Skoufis; Diana E. Woodward
    Abstract: We argue that using the Shapley value of cooperative game theory as the scheme for risk allocation among non-orthogonal risk factors is a natural way of interpreting the contribution made by each of such factors to overall portfolio risk. We discuss a Shapley value scheme for allocating risk to non-orthogonal greeks in a portfolio of derivatives. Such a situation arises, for example, when using a stochastic volatility model to capture option volatility smile. We also show that Shapley value allows for a natural method of interpreting components of enterprise risk measures such as VaR and ES. For all applications discussed, we derive explicit formulas and / or numerical algorithms to calculate the allocations.
    Date: 2021–03
  16. By: Charles-Albert Lehalle; Eyal Neuman; Segev Shlomov
    Abstract: We consider a stochastic game between three types of players: an inside trader, noise traders and a market maker. In a similar fashion to Kyle's model, we assume that the insider first chooses the size of her market-order and then the market maker determines the price by observing the total order-flow resulting from the insider and the noise traders transactions. In addition to the classical framework, a revenue term is added to the market maker's performance function, which is proportional to the order flow and to the size of the bid-ask spread. We derive the maximizer for the insider's revenue function and prove sufficient conditions for an equilibrium in the game. Then, we use neural networks methods to verify that this equilibrium holds. We show that the equilibrium state in this model experience interesting phase transitions, as the weight of the revenue term in the market maker's performance function changes. Specifically, the asset price in equilibrium experience three different phases: a linear pricing rule without a spread, a pricing rule that includes a linear mid-price and a bid-ask spread, and a metastable state with a zero mid-price and a large spread.
    Date: 2021–03
  17. By: Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics Université Paris 1 Panthéon-Sorbonne); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne - Paris School of Economics CNRS)
    Abstract: The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models
    Keywords: Domination; stable set; core; TU game
    JEL: C71
    Date: 2021–03
  18. By: Andrés Gago (Universidad Torcuato di Tella)
    Abstract: In negotiations the objectives of parties are generally in conflict. Facing this conflict can trigger negative emotions, such as nervousness, embarrassment and awkwardness, which I refer as confrontation costs. In this paper, I use a lab experiment to explore whether these costs exist and if so what their implications are. First, I show that a significant proportion of participants avoid bargaining even when it delivers higher payoffs. I find that the avoidance rate is 50% higher in face-to-face negotiations than in electronic negotiations. Second, after shutting down alternative channels, I find that the higher avoidance rate in person can be attributed to higher confrontation costs. Together, these two things make e-negotiations welfare-improving in my design, casting doubts on the general belief that face-to-face communication increases efficiency by fostering transactions. Finally, consistent with previous literature, I observe that women haggle less than men, and I find that confrontation costs can also account for this fact.
    Keywords: Bargaining, Conflict Aversion, Social Pressure, Image Concerns, Gender.
    JEL: C78 C91 D91 J16
    Date: 2020–10
  19. By: Sarah Auster; Nicola Pavoni
    Abstract: We study the delegation problem between a principal and an agent, who not only has better information about the performance of the available actions but also has superior awareness of the set of actions that are actually feasible. The agent decides which of the available actions to reveal and which ones to hide. We provide conditions under which the agent finds it optimal to leave the principal unaware of relevant options. By doing so, the agent increases the principal's cost of distorting the agent's choices and thereby increases the principal's willingness to grant him higher information rents. We also consider communication between the principal and the agent after the contract is signed and the agent receives information. We show that limited awareness of actions improves communication in such signalling games: the principal makes a coarser inference from the recommendations of the privately informed agent and accepts a larger number of his proposals.
    Keywords: Unawareness, optimal delegation, strategic disclosure
    JEL: D82 D83 D86
    Date: 2021–01
  20. By: Federico Vaccari
    Abstract: I study a multi-sender signaling game between an uninformed decision maker and two senders with common private information and conflicting interests. Senders can misreport information at a cost that is tied to the size of the misrepresentation. The main results concern the amount of information that is transmitted in equilibrium and the language used by senders to convey such information. Fully revealing and pure-strategy equilibria exist but are not plausible. I first identify sufficient conditions under which equilibria are essentially unique, robust, and always exist, and then deliver a complete characterization of these equilibria. As an application, I study the informative value of different judicial procedures.
    Date: 2021–03
  21. By: Marco Catola; Simone D'Alessandro; Pietro Guarnieri; Veronica Pizziol
    Abstract: In this study we provide a novel measurement of personal normative beliefs, empirical expectations and normative expectations in the multilevel public goods game. The objective is twofold. On the one hand, we aim at investigating whether personal and social norms are reactive to variations in the relative efficiency of the public goods. On the other hand, we aim at understating which kind of norm better explains contribution to both the public goods. In our online experiment, personal norms, as elicited by personal normative beliefs, play a crucial role. They are both more reactive to efficiency gains and more in line with contribution decisions as efficiency increases. However, social norms, as elicited by empirical expectations and normative expectations, still anchor contribution decisions to social expectations, especially when the efficiency of the related public good is relatively low. Moreover, we highlight a norm spillover effect among the public goods with the empirical expectations concerning one good impacting (negatively) the contribution to the other public good. This result reveals how norms referred to alternative reference networks may interact with each other and possibly conflict.
    Keywords: Multilevel public good game, online experiment, personal norms, social norms, social dilemma
    JEL: C9 D71 H4
    Date: 2021–03–01

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