nep-gth New Economics Papers
on Game Theory
Issue of 2018‒05‒14
twelve papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Stabilizing Cooperative Outcomes in Two-Person Games: Theory and Cases By Brams, Steven J.; Ismail, Mehmet S.
  2. Cournot tatonnement and Nash equilibrium in binary status games By Kukushkin, Nikolai S.; von Mouche, Pierre H.M.
  3. Discovery and Equilibrium in Games with Unawareness By Schipper, Burkhard C
  4. It's not always best to be first By Sela, Aner
  5. Game-theoretic model of tax evasion: analysis of agents’ interaction and optimization of tax burden By Sokolovskyi, Dmytro
  6. Gender differences in altruism on Mechanical Turk: Expectations and actual behaviour By Pablo Brañas-Garza; Valerio Capraro; Ericka Rascón Ramírez
  7. Bargaining over managerial contracts: a note By Stamatopoulos, Giorgos
  8. Empirical Equilibrium By Rodrigo A. Velez; Alexander L. Brown
  9. The Coleman-Shapley-index: Being decisive within the coalition of the interested By André Casajus; Frank Huettner
  10. Motivated Memory in Dictator Games By Charlotte Saucet; Marie Villeval
  11. Mechanisms in a Digitalized World By Gabrielle Demange
  12. The Effects of Process R&D in an Asymmetric Duopoly under Cournot and Supply Function Competitions By Saglam, Ismail

  1. By: Brams, Steven J.; Ismail, Mehmet S.
    Abstract: We analyze the 78 2 x 2 distinct strict ordinal games, 57 of which are conflict games that contain no mutually best outcome. In 19 of the 57 games (33%), including Prisoners’ Dilemma and Chicken, a cooperative outcome—one that is at least next-best for each player—is not a Nash equilibrium (NE). But this outcome is a nonmyopic equilibrium (NME) in 16 of the 19 games (84%) when the players start at this outcome and make farsighted calculations, based on backward induction; in the other three games, credible threats can induce cooperation. In two of the latter games, the NMEs are “boomerang NMEs,” whereby players have an incentive to move back and forth between two diagonally opposite NMEs, one of which is cooperative. In Prisoners’ Dilemma, the NE and one NME are not Pareto-optimal, but we conjecture that in all two-person games with strict preferences, there is at least one Pareto-optimal NME. As examples of NMEs that are not NEs, we analyze two games that plausibly model the choices of players in international relations: (i) no first use of nuclear weapons, a policy that has been adopted by some nuclear powers; and (ii) the 2015 agreement between Iran, and a coalition of the United States and other countries, that has forestalled Iran’s possible development of nuclear weapons.
    Keywords: Game theory, theory of moves, two-person games, international relations
    JEL: C70 D74 F50
    Date: 2018–04–19
  2. By: Kukushkin, Nikolai S.; von Mouche, Pierre H.M.
    Abstract: We study a rather simplified game model of competition for status. Each player chooses a scalar variable (say, the level of conspicuous consumption), and then those who chose the highest level obtain the "high" status, while everybody else remains with the "low" status. Each player strictly prefers the high status, but they also have intrinsic preferences over their choices. The set of all feasible choices may be continuous or discrete, whereas the strategy sets of different players can only differ in their upper and lower bounds. The resulting strategic game with discontinuous utilities does not satisfy the assumptions of any general theorem known as of today. Nonetheless, the existence of a (pure strategy) Nash equilibrium, as well as the "finite best response improvement property," are established.
    Keywords: status game; Cournot tatonnement; Nash equilibrium
    JEL: C72
    Date: 2018–01–28
  3. By: Schipper, Burkhard C
    Abstract: Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are ``self-destroying'' as a player's representation of the game may change after playing it once. We define discovery processes where at each state there is an extensive-form game with unawareness that together with the players' play determines the transition to possibly another extensive-form game with unawareness in which players are now aware of actions that they have discovered. A discovery process is rationalizable if players play extensive-form rationalizable strategies in each game with unawareness. We show that for any game with unawareness there is a rationalizable discovery process that leads to a self-confirming game that possesses a self-confirming equilibrium in extensive-form rationalizable strategies. This notion of equilibrium can be interpreted as steady-state of both a discovery and learning process.
    Keywords: Self-confirming equilibrium, conjectural equilibrium, extensive-form rationalizability, unawareness, extensive-form games, equilibrium, learning, discovery
    JEL: C72 D83
    Date: 2018–04
  4. By: Sela, Aner
    Abstract: We study a model with n agents, each of whom has both a linear reward function that increases in the agent's effort and an effort constraint. However, since the effort (output) of the players has a negative effect on society the designer imposes a punishment such that the agent with the highest effort who caused the greatest damage is punished. We analyze the equilibrium of this model with either symmetric or asymmetric agents. At all the equilibrium points, all the agents are active and all have positive expected payoffs. We characterize the properties of the agents' equilibrium strategies and compare them to the well-known equilibrium strategies of the all-pay auction in which the agent with the highest effort wins a prize.
    Keywords: Contests; winner's curse
    Date: 2018–04
  5. By: Sokolovskyi, Dmytro
    Abstract: The article analyzes a tax evasion problem using game-theoretic tools. The model develops a well-known Alligham–Sandmo classic model by introducing parameters of “transparency” of detected violations, of cost of control, of tax evasion and of conscientious tax payment. For that model we calculated Nash-equilibrium conditions in pure strategies. Based on this we investigated the problem of optimization of real tax burden. It is shown that curve describing the dependence between actual tax burden from declared one has not 1 (like the Laffer curve), but 3 local maxima. Those findings may contribute to better calculation of tax burden in the real economy.
    Keywords: tax evasion; game-theoretic model; Nash-equilibrium; tax burden; pure strategies; Laffer curve
    JEL: C72 H26 H30
    Date: 2018–04–30
  6. By: Pablo Brañas-Garza (Loyola Andalucia University); Valerio Capraro (Middlesex University); Ericka Rascón Ramírez (Middlesex University)
    Abstract: Whether or not there are gender differences in altruistic behavior in Dictator Game experiments has attracted considerable attention in recent years. Earlier studies found women to be more altruistic than men. However, this conclusion has been challenged by more recent accounts, which have argued that gender differences in altruistic behaviour may be a peculiarity of student samples and may not extend to random samples. Here we study gender differences in altruistic behavior and, additionally, in expectations of altruistic behaviour, in a sample of Amazon Mechanical Turk crowdworkers living in the US. In Study 1, we report a mega-analysis of more than 3,500 observations and we show that women are significantly more altruistic than men. In Study 2, we show that both women and men expect women to be more altruistic than men.
    Date: 2018–02
  7. By: Stamatopoulos, Giorgos
    Abstract: The theory of strategic managerial delegation has recently been extended by incorporating bargaining over managerial contracts (van Witteloostuijn 2007, etc). Assuming that bargaining involves only the incentive rates of managers, this line of research has shown that market outcomes (profits and social welfare) depend crucially on the intra-firm allocation of bargaining powers. In the current paper we revisit the bargaining framework assuming that negotiations involve all contractual terms (incentive rates and transfers). We show that contrary to the earlier results, the market equilibrium is independent of bargaining powers, the latter determining only the transfers. Hence the outcome of our model is identical to the outcome of the delegation model with no bargaining.
    Keywords: Strategic delegation; oligopoly; Nash bargaining; equivalence
    JEL: L13 L21
    Date: 2018–04–12
  8. By: Rodrigo A. Velez; Alexander L. Brown
    Abstract: We introduce empirical equilibrium, the prediction in a game that selects the Nash equilibria that can be approximated by a sequence of payoff-monotone distributions, a well-documented proxy for empirically plausible behavior. Then, we reevaluate implementation theory based on this equilibrium concept. We show that in a partnership dissolution environment with complete information, two popular auctions that are essentially equivalent for the Nash equilibrium prediction, can be expected to differ in fundamental ways when they are operated. Besides the direct policy implications, two general consequences follow. First, a mechanism designer may not be constrained by typical invariance properties. Second, a mechanism designer who does not account for the empirical plausibility of equilibria may inadvertently design implicitly biased mechanisms.
    Date: 2018–04
  9. By: André Casajus (HHL Leipzig Graduate School of Management); Frank Huettner (ESMT Berlin)
    Abstract: The Coleman Power of the Collectivity to Act (CPCA) is a popular statistic that re flects the ability of a committee to pass a proposal. Applying the Shapley value to this measure, we derive a new power index that indicates each voter's contribution to the CPCA. This index is characterized by four axioms: anonymity, the null voter property, transfer property, and a property that stipulates that sum of the voters' power equals the CPCA. Similar to the Shapley-Shubik index (SSI) and the Penrose-Banzhaf index (PBI), our new index emerges as the expectation of being a pivotal voter. Here, the coalitional formation model underlying the CPCA and the PBI is combined with the ordering approach underlying the SSI. In contrast to the SSI, the voters are not ordered according to their agreement with a potential bill but according to their vested interest in it. Among the most interested voters, the power is then measured in a similar way as with the PBI. Although we advocate the CSI against the PBI to capture a voter's in fluence on whether a proposal passes, the CSI gives new meaning to the PBI. The CSI is the decomposer of the PBI, splitting it into a voter's power as such and a her impact on the power of the other voters by threatening to block any proposal. We apply the index to the EU Council and the UN Security Council.
    Keywords: Decomposition, Shapley value, Shapley-Shubik index, power index, Coleman Power of the Collectivity to Act, Penrose-Banzhaf index, EU Council, UN Security Council
    JEL: C71 D60
    Date: 2018–05–08
  10. By: Charlotte Saucet (UL2 - Université Lumière - Lyon 2, GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Marie Villeval (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)
    Abstract: The memory people have of their past actions is one of the main sources of information about themselves. To study whether people retrieve their memory self-servingly, we designed an experiment in which participants have first to play binary dictator games and, second, recall the amounts allocated to the receiver. We investigate whether dictators (i) exhibit poorer recalls, (ii) overestimate more often and (iii) to a larger extent the receiver's amount when they have chosen the selfish option. We find that introducing monetary incentives for memory accuracy increases the dictators' percentage of correct recalls only when they have chosen the altruistic option. The percentage of correct recalls of the dictators is lower when they have chosen the selfish option, showing that amnesia is more likely to affect selfish than altruistic dictators. However, dictators do not bias strategically the direction and magnitude of their recalls.
    Keywords: Motivated memory, selective recalls, self-image, dictator game, experiment
    Date: 2018–04–30
  11. By: Gabrielle Demange
    Abstract: Due to computing and communication facilities, formal procedures, often referred to as ‘algorithms’, are now extensively used in public, economic and social areas. These procedures, currently at the forefront of criticisms, share some features with mechanisms as defined by economists, following Hurwicz. My aim is to investigate these relationships and to discuss some of the economic risks generated by the power of algorithms.
    Keywords: mechanisms, algorithms, algorithmic pricing and trading, social choice rule, data, Admission post-bac
    JEL: D44 D71 D82
    Date: 2018
  12. By: Saglam, Ismail
    Abstract: In this paper we attempt to explore the welfare effects of (process) R&D in an asymmetric duopoly with a homogeneous product under Cournot and supply function competitions. To this aim, we consider a two-stage perfect-information game where the duopolists compete in stage one in R&D investments and in stage two either in quantities or in supply functions. Calculating the (subgame-perfect Nash) equilibrium of this game numerically for a wide range of initial cost parameters and comparing it to the equilibrium with no R&D, we show that R&D has a positive effect on the welfares of consumers and the society as a whole. While its effect on the profits of the duopolists is also positive under the Cournot competition, it becomes negative under the supply function competition. This latter negative effect is caused by the duopolists' more aggressively investing in R&D under the supply function competition, increasing the industry output, and consequently decreasing the product price, to a harmful level for themselves. Moreover, we show that R&D always widens up the efficiency gap between the duopolists under the supply function competition, while narrowing it down under the Cournot competition.
    Keywords: Duopoly; Cournot competition; supply function competition; process R&D
    JEL: D43 L13
    Date: 2018–04–26

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