nep-gth New Economics Papers
on Game Theory
Issue of 2020‒01‒20
eighteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. A sequential bargaining protocol for land rental arrangements By Valencia-Toledo, Alfredo; Vidal-Puga, Juan
  2. Cooperation in an Uncertain and Dynamic World By Gallo, Edoardo; Riyanto, Yohanes E.; Roy, Nilanjan; Teh, Tat-How
  3. Equilibria of nonatomic anonymous games By Simone Cerreia-Vioglio; Fabio Maccheroni; David Schmeidler
  4. Strategic Issues in One-to-One Matching with Externalities By Mumcu, Ayse; Saglam, Ismail
  5. How Lies Induced Cooperation in "Golden Balls:" A Game-Theoretic Analysis By Brams, Steven J.; Mor, Ben D.
  6. Sharing the Global Benefits of Finite Natural Resource Exploitation: A Dynamic Coalitional Stability Perspective By Stéphane Gonzalez; Fatma Zahra Rostom
  7. Tax evasion and unaccounted incomes: A theoretical approach. By Sapre, Amey
  8. Affective empathy in non-cooperative games By Jorge Vasquez; Marek Weretka
  9. To snipe or not to snipe, that is the question! Transitions in sniping behaviour among competing algorithmic traders By Somayeh Kokabisaghi; Eric J Pauwels; Andre B Dorsman
  10. Optimal switching from competition to cooperation: a preliminary exploration By Raouf Boucekkine; Carmen Camacho; Benteng Zou
  11. Cartel Formation with Quality Differentiation By Iwan Bos; Marco Marini; Riccardo Saulle
  12. Timely exposure of a secret project: By B Hermans; H Hamers; Roel Leus; R Lindelauf
  13. Perfect bidder collusion through bribe and request By Jingfeng Lu; Zongwei Lu; Christian Riis
  14. Efficient allocations in double auction markets By Teemu Pennanen
  15. Coalition-Proof Risk Sharing Under Frictions By Harold L. Cole; Dirk Krueger; George J. Mailath; Yena Park
  16. Global Well-posedness of Non-Markovian Mutidimensional Superquadratic BSDE By Kihun Nam
  17. Cognitive skills, strategic sophistication, and life outcomes By Fe, Eduardo; Gill, David; Prowse, Victoria
  18. A note on the worst case approach for a market with a stochastic interest rate By Dariusz Zawisza

  1. By: Valencia-Toledo, Alfredo; Vidal-Puga, Juan
    Abstract: We consider land rental between a single tenant and several lessors. The tenant should negotiate sequentially with each lessor for the available land. In each stage, we apply the Nash bargaining solution. Our results imply that, when all land is necessary, a uniform price per unit is more favorable for the tenant than a lessor-dependent price. Furthermore, a lessor is better off with a lessor-dependent price only when negotiating first. For the tenant, lessors’ merging is relevant with lessor-dependent price but not with uniform price.
    Keywords: Bargaining; non-cooperative game; Nash solution; land rental
    JEL: C7
    Date: 2019–05–30
  2. By: Gallo, Edoardo; Riyanto, Yohanes E.; Roy, Nilanjan; Teh, Tat-How
    Abstract: We investigate how reputational uncertainty and the rate of change of the social environment interact to influence cooperation in social networks. Reputational uncertainty significantly decreases cooperation and welfare, induces more forgiveness toward defectors, and promotes opportunistic play. Compared to reputational uncertainty, a fast-changing social environment only causes a second-order qualitative increase in cooperation by making individuals more lenient in imposing a network-punishment (link removal). The interaction between reputational uncertainty and a fast-changing social environment induces more lenient strategies by reducing the frequency of action-punishment (retaliatory defection). Although neither of them affects the aggregate network metrics, their interaction decreases homophily among cooperators.
    Keywords: Cooperation, experiments, prisoner's dilemma, uncertainty, repeated games, networks
    JEL: C72 C73 C92 D8
    Date: 2019–12–30
  3. By: Simone Cerreia-Vioglio; Fabio Maccheroni; David Schmeidler
    Abstract: We add here another layer to the literature on nonatomic anonymous games started with the 1973 paper by Schmeidler. More specifically, we define a new notion of equilibrium which we call "-estimated equilibrium and prove its existence for any positive ". This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk-Nash. This augmented scope is our main motivation. At the same time, our approach also resolves some conceptual problems present in Schmeidler (1973), pointed out by Shapley. In that paper the existence of pure-strategy Nash equilibria has been proved for any nonatomic game with a continuum of players, endowed with an atomless countably additive probability. But, requiring Borel measurability of strategy profiles may impose some limitation on players’ choices and introduce an exogenous dependence among players’ actions, which clashes with the nature of noncooperative game theory. Our suggested solution is to consider every suset of players as measurable. This leads to a nontrivial purely finitely additive component which might prevent the existence of equilibria and requires a novel mathematical approach to prove the existence of "-equilibria.
    Date: 2019
  4. By: Mumcu, Ayse; Saglam, Ismail
    Abstract: We consider strategic issues in one-to-one matching with externalities. We show that no core (stable) mechanism is strategy-proof, extending an impossibility result of Roth (1982) obtained in the absence of externalities. Moreover, we show that there are no limits on successful manipulation of preferences by coalitions of men and women, in contrast with the result of Demange et al. (1987) obtained in the absence of externalities.
    Keywords: One-to-one matching; externalities; stability; core; strategic manipulation.
    JEL: C71 C78 D62
    Date: 2019–12–18
  5. By: Brams, Steven J.; Mor, Ben D.
    Abstract: We analyze a particular episode of a popular British TV game show, “Golden Balls,” in which one of the two contestants lied about what he intended to do, which had the salutary effect of inducing both contestants to cooperate in what is normally a Prisoners' Dilemma (PD), wherein one or both contestants usually defected. This “solution” to PD assumes that the liar desired to be honorable in fulfilling his pledge to split the jackpot if he won but, surprisingly, he achieved this end without having to do so, astonishing the audience and receiving its acclaim. We note that this action has a biblical precedent in King Solomon’s decision to cut a baby in two.
    Keywords: Lying in games; Prisoners' Dilemma; King Solomon; Honor
    JEL: C72
    Date: 2019–12
  6. By: Stéphane Gonzalez (Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint- Etienne); Fatma Zahra Rostom (Université Paris 1, Centre d’Economie de la Sorbonne, Chaire Energie et Prospérité)
    Abstract: The article explores the implications of natural resource scarcity in terms of global cooperation and trade. We investigate whether there exist stable international long-term agreements that take into account the disparities between countries in terms of geological endowments and productive capacity, while caring about future generations. For that purpose, we build an original cooperative game framework, where countries can form coalitions in order to optimize their discounted consumption stream in the long-run, within the limits of their stock of natural resources. We use the concept of the recursive core that satisfies both coalitional stability and time consistency. We show that this set is nonempty, stating that an international long-term agreement along the optimal path will be self-enforcing. The presented model can be viewed as a tool to refresh the common look at the North-South opposition and sets the conceptual framework for the exploration of a fair sharing of the fruits of global economic growth.
    Keywords: Non-renewable natural resources, Cooperative games, Recursive core
    JEL: C71 C61 F42 Q20 Q32 Q56
    Date: 2019
  7. By: Sapre, Amey (National Institute of Public Finance and Policy)
    Abstract: This paper analyzes the problem of tax evasion by incorporating a simple game theoretic framework wherein an individual is confronted with the decision of declaring income for taxation. The model is a re-formulation of Allingham Sandmo (1972) and Srinivasan (1973) original single period decision making problem and extends it to to a repeated game involving a tax payer and a tax authority. The game theoretic results shows that probability of audit and penalty rate are inversely related and that beyond a threshold penalty rate, the tax payer has no incentive to evade. In an infinitely repeated game setting, first, the threat of audit in all future periods acts as a deterrent to evasion and second, the result provides some intuitive understanding of the role of patience and equilibrium strategies in a long repetitive engagement that supports cooperation and prevents deviations.
    Keywords: Tax evasion ; Repeated game ; Public Finance
    JEL: C73 H26
    Date: 2019–12
  8. By: Jorge Vasquez (Smith University; Group for Research in Applied Economics (GRAPE)); Marek Weretka (Group for Research in Applied Economics (GRAPE); University of Wisconsin-Madison)
    Abstract: According to psychology, affective empathy is one of the key processes governing human interactions. It refers to the automatic transmission and diffusion of emotions in response to others' emotions, which gives rise to emotional contagion. Contrary to other forms of empathy, affective empathy has received little attention in economics. In this paper, we augment the standard game-theoretic framework by allowing players to affectively empathize. Players' utility functions depend not only on the strategy prole being played, but also on the realized utilities of other players. Thus, players' realized utilities are interdependent, capturing emotional contagion. We offer a solution concept for these empathetic games and show that the set of equilibria is non-empty and, generically, finite. Motivated by psychological evidence, we analyze sympathetic and antipathetic games. In the former, players' utilities increase in others' realized utilities, capturing unconditional friendship; whereas in the latter the opposite holds, resembling hostility.
    Keywords: affective empathy, emotional contagion, Interdependent utilities, non-paternalistic preferences
    JEL: D64 D90 D91
    Date: 2020
  9. By: Somayeh Kokabisaghi; Eric J Pauwels; Andre B Dorsman
    Abstract: In this paper we re-analyse the transition from sure to probabilistic sniping as explored in Menkveld and Zoican [14]. In that paper, the authors introduce a stylized version of a competitive game in which high frequency traders (HFTs) interact with each other and liquidity traders. The authors show that risk aversion plays an important role in the transition from sure to mixed (or probabilistic) sniping. In this paper, we re-interpret and extend these conclusions in the context of repeated games and highlight some differences in results. In particular, we identify situations in which probabilistic sniping is genuinely profitable that are qualitatively different from the ones obtained in [14]. Keywords: algorithmic trading,sniping, electronic exchange,high-frequency traders,Nash equilibrium,repeated games,bandits, subgame-perfect equilibrium,transition
    Date: 2019–12
  10. By: Raouf Boucekkine (Aix-Marseille School of Economics [Aix-Marseille Université] - Centre de la Vieille Charité [Aix-Marseille Université] - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique); Carmen Camacho (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PSE - Paris School of Economics); Benteng Zou ( - Université du Luxembourg)
    Abstract: In this paper, we tackle a generic optimal regime switching problem where the decision making process is not the same from a regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a two- stage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for open-loop strategies with a linear state equation and linear-quadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using the- oretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss the reverse switching.
    Keywords: Cooperation,competition,dynamic games,multi-stage optimal control
    Date: 2020–01
  11. By: Iwan Bos; Marco Marini (Department of Social and Economic Sciences, Sapienza University of Rome and CREI, Italy); Riccardo Saulle (DSEA, University of Padova, Italy)
    Abstract: Research on collusion in vertically differentiated markets is conducted under one or two potentially restrictive assumptions. Either there is a single industry-wide cartel or costs are assumed to be independent of quality or quantity. We explore the extent to which these assumptions are indeed restrictive by relaxing both. For a wide range of coalition structures, profit-maximizing cartels of any size price most of their lower quality products out of the market as long as production costs do not increase too much with quality. If these costs rise sufficiently, however, then market share is maintained for all product variants. All cartel sizes may emerge in equilibrium when exclusively considering individual deviations, but the industry-wide cartel is the only one immune to deviations by coalitions of members. Overall, our findings suggest that firms have a strong incentive to coordinate prices when the products involved are vertically differentiated.
    Keywords: Cartel Formation, Collusion, Vertical Differentiation, Endogenous Coalition Formation, Industry-wide Cartel, Partial Cartels.
    JEL: D42 D43 L1 L12 L13 L41
    Date: 2019–12
  12. By: B Hermans; H Hamers; Roel Leus; R Lindelauf
    Abstract: A defender wants to detect as quickly as possible whether some attacker is secretly conducting a project that could harm the defender. Security services, for example, need to expose a terrorist plot in time to prevent it. The attacker, in turn, schedules his activities so as to remain undiscovered as long as possible. One pressing question for the defender is: which of the project’s activities to focus intelligence efforts on? We model the situation as a zero-sum game, establish that a late-start schedule defines a dominant attacker strategy, and describe a dynamic program that yields a Nash equilibrium for the zero-sum game. Through an innovative use of cooperative game theory, we measure the harm reduction thanks to each activity’s intelligence effort, obtain insight into what makes intelligence effort more effective, and show how to identify opportunities for further harm reduction. We use a detailed example of a nuclear weapons development project to demonstrate how a careful trade-off between time and ease of detection can reduce the harm significantly.
    Date: 2018–10
  13. By: Jingfeng Lu; Zongwei Lu; Christian Riis
    Abstract: We study collusion in a second price auction with two bidders in a dynamic environment. One bidder can make a take-it-or-leave-it collusion proposal, which consists of both an offer and a request of bribes, to the opponent. We show there always exists a robust equilibrium in which the collusion success probability is one. In the equilibrium, the interim expected payoff of the collusion initiator Pareto dominates the counterpart in any robust equilibria of the single-option model (Es\"{o} and Schummer (2004)) and any other separating equilibria in our model.
    Date: 2019–12
  14. By: Teemu Pennanen
    Abstract: This paper proposes a simple descriptive model for discrete-time double auction markets of divisible assets. As in the classical models of exchange economics, we consider a finite set of agents described by their initial endowments and preferences. Instead of the classical Walrasian-type market models, however, we assume that all trades take place in double auctions where the agents communicate through sealed limit orders for buying and selling. We find that, in repeated call auctions, nonstrategic bidding leads to a sequence of allocations that converges to individually rational Pareto allocations.
    Date: 2020–01
  15. By: Harold L. Cole (University of Pennsylvania); Dirk Krueger (University of Pennsylvania); George J. Mailath (University of Pennsylvania); Yena Park (University of Rochester)
    Abstract: We analyze e?cient risk-sharing arrangements when coalitions may deviate. Coalitions form to insure against idiosyncratic income risk. Self-enforcing contracts for both the original coalition and any deviating coalition rely on a belief in future cooperation, and we treat the contracting conditions of original and deviating coalitions symmetrically. We show that better belief coordination (higher social capital) tightens incentive constraints since it facilitates both the formation of the original as well as a deviating coalition. As a consequence, the payo? of successfully formed coalitions might be declining in the degree of belief coordination and equilibrium allocations might feature resource burning or utility burning.
    Keywords: Financial Coalition, Limited Enforcement, Risk Sharing, Coalition-Proof Equi-librium
    JEL: E21 G22 D11 D91
    Date: 2019–01–08
  16. By: Kihun Nam
    Abstract: Using purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backward stochastic differential equations and backward iterations of the superquadratic BSDE. The superquadratic BSDE in this article includes quadratic BSDEs appear in stochastic differential game and price impact model. Our result also provides the well-posedness of a system of path-dependent quasilinear PDE that generalizes Ladyzhenskaia and Uraltseva (1968).
    Date: 2019–12
  17. By: Fe, Eduardo (University of Manchester); Gill, David (Purdue University); Prowse, Victoria (Purdue University)
    Abstract: We investigate how childhood cognitive skills affect strategic sophistication and adult outcomes. In particular, we emphasize the importance of childhood theory-of-mind as a cognitive skill. We collected experimental data from more than seven hundred children in a variety of strategic interactions. First, we find that theory-of-mind ability and cognitive ability both predict level-k behavior. Second, older children respond to information about the cognitive ability of their opponent, which provides support for the emergence of a sophisticated strategic theory-of-mind. Third, theory-of-mind and age strongly predict whether children respond to intentions in a gift-exchange game, while cognitive ability has no influence, suggesting that different measures of cognitive skill correspond to different cognitive processes in strategic situations that involve understanding intentions. Using the ALSPAC birth-cohort study, we find that childhood theory-of-mind and cognitive ability are both associated with enhanced adult social skills, higher educational participation, better educational attainment, and lower fertility in young adulthood. Finally, we provide evidence that school spending improves theory-of-mind in childhood.
    Keywords: Cognitive skills; theory-of-mind; cognitive ability; fluid intelligence; children; experiment; strategic sophistication; level-k; bounded rationality; non-equilibrium thinking; intentions; gift-exchange game; competitive game; strategic game; ALSPAC; social skills; adult outcomes; life outcomes; education; fertility; labor market; wages; employment; school spending; childhood intervention. JEL Classification: C91; D91; J24
    Date: 2019
  18. By: Dariusz Zawisza
    Abstract: We solve robust optimization problem and show the example of the market model for which the worst case measure is not a martingale measure. In our model the instantaneous interest rate is determined by the Hull-White model and the investor employs the HARA utility to measure his satisfaction.To protect against the model uncertainty he uses the worst case measure approach. The problem is formulated as a stochastic game between the investor and the market from the other side. PDE methods are used to find the saddle point and the precise verification argument is provided.
    Date: 2020–01

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