nep-gth New Economics Papers
on Game Theory
Issue of 2017‒12‒18
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Liability Games By Csoka, Péter; Herings, P. Jean-Jacques
  2. Nash-2 equilibrium: selective farsightedness under uncertain response By Sandomirskaia, Marina
  3. Aggregation in Networks By Nizar Allouch
  4. Algorithms for cautious reasoning in games* By Asheim, Geir B.; Perea, Andrés
  5. Sequential Lottery Contests with Multiple Participants By Nava Kahana; Doron Klunover
  6. Instability in the Voluntary Contribution Mechanism with a Quasi-linear Payoff Function: An Experimental Analysis By Jun Feng; Tatsuyoshi Saijo; Junyi Shen; Xiangdong Qin
  7. Refugee Matching as a Market Design Application By Andersson, Tommy
  8. On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods By Gentry, Matthew; Komarova, Tatiana; Schiraldi, Pasquale; Shin, Wiroy
  9. Nudging with heterogeneity in terms of environmental sensitivity : a public goods experiment in networks. By Benjamin Ouvrard; Anne Stenger
  10. Tournaments with subsequent group stages are incentive incompatible By Csató, László
  11. Escalation in Dynamic Conflict: On Beliefs and Selection By Kai A. Konrad; Florian Morath
  12. The Multiplier Effect in Two-Sided Markets with Bilateral Investments By Deniz Dizdar; Benny Moldovanu; Nora Szech
  13. Collective Action in Games as in Life: Experimental Evidence from Canal Cleaning in Haiti By Abbie Turiansky
  14. The degree measure as utility function over positions in networks By René Van den Brink; Agnieszka Rusinowska
  15. Resource Allocation with Warranties in Claims Problems By Giménez-Gómez, José-Manuel; Peris, Josep E.; Solís-Baltodano, María-José
  16. Implications of multilateral tariff bindings on the formation of preferential trade agreements and quest for global free trade By Nken, Moïse; Yildiz, Halis Murat
  17. Eternal Peace in the Tug-of-War? By Samuel Häfner; Kai A. Konrad
  18. Matching between Students and Universities: What are the Sources of Inequalities of Access to Higher Education? By Ilya Prakhov; Denis Sergienko
  19. Competition, Information and Cooperation. By Lotito, Gianna; Migheli, Matteo; Ortona, Guido
  20. Prize allocation and incentives in team contests By Crutzen, Benoît SY; Flamand, Sabine; Sahuguet, Nicolas
  21. Brand positioning and consumer taste information By Arcan Nalca,; Tamer Boyaci,; Saibal Ray

  1. By: Csoka, Péter (corvinus university of budapest); Herings, P. Jean-Jacques (General Economics 1 (Micro))
    Abstract: A firm has liabilities towards a group of creditors. We analyze the question of how to distribute the asset value of the firm among the creditors and the firm itself. Compared to standard bankruptcy games as studied in the game theory literature, we introduce the firm as an explicit player and define a new class of transferable utility games called liability games. Liability games are superadditive, constant sum, partially convex, and partially concave. The core of a liability game is empty if and only if the firm is insolvent and has multiple positive liabilities. We analyze the nucleolus of the game and show that allocating the asset value of the firm using the nucleolus satisfies efficiency, non-negativity, and liabilities boundedness. We prove that at the nucleolus, the firm gets a strictly higher amount than its stand-alone value if and only if the firm is insolvent and has multiple positive liabilities. The firm is using the threat to pay others to get debt forgiveness and is able to keep a positive amount of its assets. We provide conditions under which the nucleolus coincides with a generalized truncated proportional rule, assigning a non-negative payment to the firm and distributing the remainder in proportion to the liabilities, truncated by the asset value of the firm.
    Keywords: insolvency, debt forgiveness, bankruptcy games, nucleolus, proportional rule
    JEL: C71 G10
    Date: 2017–12–07
  2. By: Sandomirskaia, Marina
    Abstract: This paper provides an extended analysis of an equilibrium concept for non-cooperative games with boundedly rational players: a Nash-2 equilibrium. Players think one step ahead and account all profitable responses of player-specific subsets of opponents because of both the cognitive limitations to predict everyone's reaction and the inability to make more deep and certain prediction even about a narrow sample of agents. They cautiously reject improvements that might lead to poorest profit after some possible reasonable response. For $n$-person games we introduce a notion of reflection network consisting of direct competitors to express the idea of selective farsightedness. For almost every 2-person game with a complete reflection network, we prove the existence of Nash-2 equilibrium. Nash-2 equilibrium sets in the models of price and quantity competition, and in Tullock's rent-seeking model with 2 players are obtained. It is shown that such a farsighted behavior may provide a strategic support for tacit collusion.
    Keywords: Iterated thinking; Improving deviation; Direct competitor; Heterogeneous farsightedness; Tacit collusion
    JEL: C72 D03 D43 D70 L13
    Date: 2017–12–05
  3. By: Nizar Allouch
    Abstract: In this paper, we show that a concept of aggregation can hold in network games. Breaking up large networks into smaller pieces, which can be replaced by representative players, leads to a coarse-grained description of strategic interactions. This method of summarizing complex strategic interactions by simple ones can be applied to compute Nash equilibria. We also provide an application to public goods in networks to show the usefulness of our results. In particular, we highlight network architectures that cannot prevent free-riding in public good network games. Finally, we show that aggregation enhances the stability of a Nash equilibrium.
    Keywords: aggregation; modular decomposition; network games; public goods; stability
    JEL: C72 D31 D85 H41
    Date: 2017–12
  4. By: Asheim, Geir B. (Dept. of Economics, University of Oslo); Perea, Andrés (Maastricht University)
    Abstract: We provide comparable algorithms for the Dekel-Fudenberg procedure, iterated admissibility, proper rationalizability and full permissibility by means of the concepts of preference restrictions and likelihood orderings. We apply the algorithms for comparing iterated admissibility, proper rationalizability and full permissibility, and provide a sufficient condition under which iterated admissibility does not rule out properly rationalizable strategies. Finally, we use the algorithms to examine an economically relevant strategic situation, namely a bilateral commitment bargaining game.
    Keywords: Non-cooperative games; proper rationalizability; iterated admissibility; bargaining
    JEL: C72 C78
    Date: 2017–10–01
  5. By: Nava Kahana; Doron Klunover
    Abstract: The literature on aggregative games, which has been applied in the study of contests, has focused on simultaneous games. We apply aggregative games techniques in a novel fashion in the analysis of sequential lottery contests with n players. It is shown that: (1) there exists a unique subgame perfect equilibrium in pure strategies, and (2) unlike in the case of a small contest, aggregate expenditure in a large contest is lower than in the corresponding simultaneous contest.
    Keywords: Aggregative games, Sequential Contests, Subgame Perfect Equilibrium
    JEL: C72 D43 L13
    Date: 2017–04
  6. By: Jun Feng; Tatsuyoshi Saijo (Research Institute for Humanity and Nature); Junyi Shen (Research Institute for Economics and Business Administration, Kobe University); Xiangdong Qin (Antai College of Economics and Management,Shanghai Jiaotong University)
    Abstract: We conduct experiments to investigate the convergence of contributions in the voluntary contribution mechanism (VCM) with two quasi-linear payoff functions. One is linear with respect to private goods and nonlinear with respect to public goods; we call it “QL1.†The other is linear with respect to public goods and nonlinear with respect to private goods; we call it “QL2.†The system with QL1, built on the assumption of self-interested players and myopic Cournot best response dynamics, is not stable, but the system with QL2 has a dominant Nash equilibrium. This theoretical result predicts a “pulsing†of contributions in the VCM with QL1. Our experimental observations demonstrate that individual contributions are certainly converging to the dominant Nash equilibrium in the experiment with QL2. In the experiments with QL1, however, the dispersion of individual contributions increases progressively with repeated trials, and the contributions are still volatile in the experiments’ last periods, although we do not find a clearly unstable pulsing in the group’s total contribution.
    Keywords: Instability, public goods game, lab experiment, voluntary contribution mechanism, conditional cooperator
    JEL: H41
    Date: 2017–12
  7. By: Andersson, Tommy (Department of Economics, Lund University)
    Abstract: This note contains a few brief remarks on the similarities and differences between some standard market design applications (e.g., kidney exchange and school choice) and the refugee assignment problem. The main conclusion is that the refugee assignment problem is more complex in some dimensions than many of the standard market design applications. Consequently, classical mechanisms cannot be used to solve the problem and more research is needed to, e.g., understand how to model preferences, and how to define relevant axioms and multidimensional constraints.
    Keywords: forced migration; asylum seekers; refugee assignment; matching; market design
    JEL: C78 F22
    Date: 2017–08–12
  8. By: Gentry, Matthew; Komarova, Tatiana; Schiraldi, Pasquale; Shin, Wiroy
    Abstract: We explore existence and properties of equilibrium when N>1 bidders compete for L>1 objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for L objects against many local bidders who bid for single objects only, highlighting the step in this extension which fails with multiple global bidders. We therefore instead consider an alternative equilibrium with endogenous tie-breaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that this exists in general. Finally, we explore efficiency in simultaneous auctions with symmetric bidders, establishing novel sufficient conditions under which inefficiency in expectation approaches zero as the number of bidders increases.
    Keywords: simultaneous auctions; complementarities; synergies; equilibria existence; efficiency; multi-object auctions; monotone strategies
    JEL: C72 D44
    Date: 2017–12
  9. By: Benjamin Ouvrard; Anne Stenger
    Abstract: We propose an experiment to test whether the reaction to a nudge implemented in a network depends on the network structure and on the sensitivity of individuals to the environment. After having elicited the sensitivity of subjects to environmental matters, the subjects played a public goods game in a network. The first ten periods served as a baseline. A nudge (announcement of the socially optimal level of investment) was then implemented both under complete information (the content of the nudge takes individuals’ position into account) and under incomplete information (the nudge cannot rely on individuals’ positions). Nudge implementation induces a higher coordination on the social optimum in the circle network for the most sensitive subjects. In the star network, the targeted nudge induces a decrease in the level of investments for the least sensitive subjects. Thus, nudge implementation should target specific individuals in specific network structures.
    Keywords: environmental sensitivity; inequity aversion; networks; nudge; public goods experiment.
    JEL: C72 C91 H41 Q50
    Date: 2017
  10. By: Csató, László
    Abstract: We discuss the strategy-proofness of multistage tournaments. In a tournament with subsequent group stages, players are divided into groups in the preliminary and main rounds, where they play pairwise matches against each other. The higher ranked players qualify to the next stage such that matches are not repeated in the main round if two qualified players have already faced in the preliminary round. Players prefer to carry over better results to the main round, provided that they qualify. It is shown that these tournament systems, widely used in handball, are incentive incompatible. We also present some historical examples where a team was ex ante not interested in winning by a high margin.
    Keywords: OR in sport; tournament ranking; handball; strategy-proofness; manipulation
    JEL: C44 D71 L83
    Date: 2017–12–12
  11. By: Kai A. Konrad; Florian Morath
    Abstract: We study a dynamic multi-stage contest that resolves in each stage only with a given probability. Assuming that there is unobservable heterogeneity in intrinsic motivations we derive properties of the equilibrium efforts across the different stages. Whereas in the corresponding complete information benchmark equilibrium efforts are stable across the stages, uncertainty about the type distribution of possible opponents generates learning. We identify reasons for dynamic adjustments of efforts caused by belief formation and updating and by selection of certain types into continuing conflict. A corresponding experimental setup provides evidence for escalation of efforts in later stages, for type heterogeneity, for belief formation and belief updating, and for selfselection. Overall, our results suggest the importance of an appropriate benchmark model when testing predictions on behavior in conflict or related strategic interactions.
    Keywords: Dynamic conflict, lottery contest, heterogeneity, incomplete information, uncertainty, escalation, beliefs, selection, learning, experiment
    JEL: C90 D72 D74 D83
    Date: 2017–08
  12. By: Deniz Dizdar (University of Montreal); Benny Moldovanu (University of Bonn); Nora Szech (Karlsruher Institut für Technologie)
    Abstract: Agents in a finite two-sided market make costly investments and are then matched assortatively on the basis of these investments. Besides signaling complementary, privately known types, investments also generate benefits for partners. Our analysis sheds light on 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 rank within their own market side and on their uncertainty about the types and investments of potential partners. Nevertheless, some key features of the effect are independent of the type distributions. We quantify how the strength of the multiplier effect depends on market size, and we study how it interacts with other important factors of the environment such as the costs and benefits of investment and the signaling incentives induced by the competition for more desirable partners. We use our results to characterize equilibrium utilities in large markets for cases in which investments are either partially wasteful or correspond to TU transfers, and also to provide bounds on the hold-up problem in small markets with productive investments.
    Keywords: matching, signaling, Investment, multiplier effect
    JEL: C78 D44 D82
    Date: 2017–11
  13. By: Abbie Turiansky
    Abstract: This paper explores the impact of farmers’ exposure to a collective action dilemma in a framed public goods game on their real-world contributions to a public good. Farmers who were randomly selected to play the public goods games were 47% more likely than the control group to volunteer to clean shared irrigation canals.
    Keywords: Haiti, public goods, framed field experiments, behavioral economic nudges
    JEL: F Z
  14. By: René Van den Brink (Department of Econometrics and Tinbergen Institute - VU University); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)
    Abstract: In this paper, we connect the social network theory on centrality measures to the economic theory of preferences and utility. Using the fact that networks form a special class of cooperative TU-games, we provide a foundation for the degree measure as a von Neumann-Morgenstern expected utility function reflecting preferences over being in different positions in different networks. The famous degree measure assigns to every position in a weighted network the sum of the weights of all links with its neighbours. A crucial property of a preference relation over network positions is neutrality to ordinary risk. If an expected utility function over network positions satisfies this property and some regularity properties, then it must be represented by a utility function that is a multiple of the degree centrality measure. We show this in three steps. First, we characterize the degree measure as a centrality measure for weighted networks using four natural axioms. Second, we relate these network centrality axioms to properties of preference relations over positions in networks. Third, we show that the expected utility function is equal to a multiple of the degree measure if and only if it represents a regular preference relation that is neutral to ordinary risk. Similarly, we characterize a class of affine combinations of the outdegree and indegree measure in weighted directed networks and deliver its interpretation as a von Neumann-Morgenstern expected utility function.
    Abstract: Dans cet article, nous associons la théorie des réseaux sociaux sur les mesures de centralité à la théorie économique des préférences et de l'utilité. En utilisant le fait que les réseaux forment une classe spéciale de jeux TU coopératifs, nous fournissons une base pour la mesure de degré en tant que fonction d'utilité attendue de von Neumann-Morgenstern reflétant les préférences en ce qui concerne les positions différentes dans différents réseaux. La célèbre mesure de degré attribue à chaque position d'un réseau pondéré la somme des poids de tous les liens avec ses voisins. Une propriété cruciale d'une relation de préférence sur les positions du réseau est la neutralité face au risque ordinaire. Si une fonction d'utilité attendue sur les positions du réseau satisfait cette propriété et certaines propriétés de régularité, elle doit être représentée par une fonction d'utilité qui est un multiple de la mesure de centralité de degré. Nous montrons cela en trois étapes. Tout d'abord, nous caractérisons la mesure du degré en tant que mesure de centralité pour les réseaux pondérés utilisant quatre axiomes naturels. Deuxièmement, nous rapportons ces axiomes de centralité de réseau aux propriétés des relations de préférence par rapport aux positions dans les réseaux. Troisièmement, nous montrons que la fonction d'utilité attendue est égale à un multiple de la mesure de degré si et seulement si elle représente une relation de préférence régulière qui est neutre au risque ordinaire. De même, nous caractérisons une classe de combinaisons affines de la mesure impartiale et indépendante dans les réseaux pondérés orientés et fournissons son interprétation en tant que fonction d'utilité attendue de von Neumann-Morgenstern.
    Keywords: Weighted network, network centrality, utility function, degree centrality,von Neumann-Morgenstern expected utility function, cooperative TU-game, weighted directed network,Réseau pondéré,centralité,fonction d'utilité,centralité de degré,fonction d'utilité attendue de von Neumann-Morgenstern,jeu coopératif,réseau pondéré orienté
    Date: 2017–07
  15. By: Giménez-Gómez, José-Manuel (Universitat Rovira i Virgili, Departament d'Economia and CREIP); Peris, Josep E. (University of Alicante, D. Quantitative Methods and Economic Theory); Solís-Baltodano, María-José (Universitat Rovira i Virgili, Departament d'Economia and CREIP)
    Abstract: The establishing of warranties in order to ensure some minimum awards to each agent involved in an allocation (claims) problem has been analyzed in the body of literature by introducing lower bounds. When focusing on claims problems, four main lower bounds on awards have been defined: the minimal right (Curiel et al., 1987), the fair lower bound (Moulin, 2002), securement (Moreno-Ternero and Villar, 2004) and the min lower bound (Dominguez, 2013). The current approach analyzes the effect of requiring the aforementioned lower bounds in an allocation mechanism. We compare the mechanisms thus obtained together with the use of some additional properties. By doing so, we show that there is a correspondence between lower bounds and claims rules, i.e., associated to each particular lower bound, we find a particular claims rule. Consequently, we provide new characterizations for the constrained equal awards rule, as well as the Ibn Ezra proposal. Finally, a dual analysis, by using upper bounds in awards, provides characterizations of the dual rules of the previous ones: the constrained equal losses rule and the dual of the Ibn Ezra rule.
    Keywords: Claims problems; Warranties; Lower bounds; Claims rules
    JEL: C71 D63 D71
    Date: 2017–12–12
  16. By: Nken, Moïse; Yildiz, Halis Murat
    Abstract: Using an endogenous preferential trade agreement (PTA) formation model under all possible multilaterally negotiated bound tariff rates, we examine the effects of multilateral trade liberalization on the role of PTAs in achieving global free trade. We first show that, when countries are completely symmetric, no country has an incentive to unilaterally deviate (free ride) from free trade network while exclusion incentives arise when bound tariffs are sufficiently low. Due to the relatively flexible nature of the FTA formation, such exclusion incentives go unexercised and free trade always obtains as the coalition-proof Nash equilibrium (CPNE) of the FTA game. However, such flexibility does not exist under the CU game and thus countries are able to exercise the exclusion incentive and free trade fails to be CPNE when the bound tariff rates are sufficiently low. We then consider a scenario where countries are asymmetric with respect to their comparative advantage. The country with a weaker comparative advantage has an incentive to free ride on trade liberalization of the other two countries and lower bound tariff rates disciplines this incentive via limiting the ability to set optimal tariffs. As a result, multilateral free trade is more likely to be a CPNE as the multilateral negotiated bound tariff rates decline. This result provides support for the idea that multilateral trade liberalization acts as a complement to the FTA formation in achieving global free trade.
    Keywords: Bound Tariff Rates, Coalition proof Nash equilibrium, Free Trade Agreement, Customs Union, Exclusion Incentive, Free Riding Incentive.
    JEL: F1 F11 F13 F15
    Date: 2017–12–07
  17. By: Samuel Häfner; Kai A. Konrad
    Abstract: The tug-of-war between single players is known to have a non-cooperative Markov-perfect equilibrium in which both players expend zero efforts and neither player drives the Markov process to one of the terminal states. We show that these peaceful outcomes vanish if the single players are replaced by teams with team members permanently assigned to the different Markov states and interacting pairwise in an all-pay auction. The reason for this phenomenon is that the members of the teams can externalize future effort costs while the single players cannot. Our analysis also highlights the impact of the discount factor on the expected trajectory of the tug-of-war, the dynamics of the expected efforts, and the degree of rent dissipation.
    Keywords: Contests, Teams, Tug-of-War
    JEL: D74 D72
    Date: 2016–10–18
  18. By: Ilya Prakhov (National Research University Higher School of Economics); Denis Sergienko (National Research University Higher School of Economics)
    Abstract: It is assumed that a perfect balance between student academic achievement and university quality is beneficial both for students and higher education institutions (HEIs). Matching theory predicts the existence of perfect matching between the two groups in the absence of transaction costs associated with university enrollment. However, in this study we show cases of mismatch situations in Russia under the Unified State Exam (USE) – the standardized student admission mechanism. This research studies the reasons for this phenomenon for minimal transaction costs and the emergence of unequal access to HEIs. Based on data on Moscow high school graduates who entered university, the determinants of the mismatch between the quality of universities and applicant abilities are assessed. It is shown that although in most cases favorable matching results are established, the individual student achievement results themselves are subject to the influence of school and family characteristics. Thus, inequality of access can be formed at stages preceding HEI enrollment
    Keywords: matching, mismatch, admission, accessibility of higher education, the Unified State Exam
    JEL: I21 I24 I28
    Date: 2017
  19. By: Lotito, Gianna; Migheli, Matteo; Ortona, Guido (University of Turin)
    Abstract: We inquire experimentally whether rivalry induced by competition has any impact on the individual voluntary contribution to a public good. Participants perform a task and are remunerated according to two schemes, a noncompetitive and a competitive one, then they play a standard public goods game. In the first scheme participants earn a flat remuneration, in the latter they are ranked according to their performance and remunerated accordingly. Information about ranking and income, before the game is played, varies across three different treatments. We find that competition per se does not affect the amount of contribution. The time spent to choose how much to contribute is negatively correlated with the decision of cooperating fully. The main result is that full information about the relative performance in the competitive environment enhances cooperation, while partial information reduces it.
    Date: 2017–09
  20. By: Crutzen, Benoît SY; Flamand, Sabine; Sahuguet, Nicolas
    Abstract: We study a contest between teams that compete for multiple indivisible prizes. Team output is a CES function of all the team members' efforts. We use a generalized Tullock contest success function to allocate prizes between teams. We study how different intra-team prize allocation rules impact team output. We consider an egalitarian rule that gives all members the same chance of receiving a prize, and a list rule that sets ex-ante the order in which members receive a prize. The convexity of the cost of effort function and the complementarity of individual efforts determine which rule maximizes team output and success. Our results speak to many real world situations, such as elections, contests for the allocation of local public goods and the internal organization of firms.
    Date: 2017–12
  21. By: Arcan Nalca, (Smith School of Business, Queen's University); Tamer Boyaci, (ESMT European School of Management and Technology); Saibal Ray (Desautels Faculty of Management, McGill University)
    Abstract: In this paper, we study how a retailer can benefit from acquiring consumer taste information in the presence of competition between the retailers store brand (SB) and a manufacturers national brand (NB). In our model, there is ex-ante uncertainty about consumer preferences for distinct product features, and the retailer has an advantage in resolving this uncertainty because of his close proximity to consumers. Our focus is on the impact of the retailers information acquisition and disclosure strategy on the positioning of the brands. Our analysis reveals that acquiring taste information allows the retailer to make better SB positioning decisions. Information disclosure, however, enables the manufacturer to make better NB positioning decisions – which in return may benefit or hurt the retailer. For instance, if a particular product feature is quite popular, then it is beneficial for the retailer to incorporate that feature into the SB, and inform the manufacturer so that the NB also includes this feature. Information sharing, in these circumstances, benefits both the retailer and the manufacturer, even though it increases the intensity of competition between the brands. But, there are situations in which the retailer refrains from information sharing so that a potentially poor positioning decision by the NB makes the SB the only provider of the popular feature. The retailer always benefits from acquiring information. However, it is beneficial to the manufacturer only if the retailer does not introduce an SB due to the associated high fixed cost.
    Keywords: supply chain management, uncertain consumer taste, product introduction, product positioning, store brands, national brands, information acquisition, information sharing, vertical difierentiation, horizontal difierentiation
    Date: 2017–01–25

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