nep-gth New Economics Papers
on Game Theory
Issue of 2018‒10‒08
23 papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Sion's mini-max theorem and Nash equilibrium in a multi-players game with two groups which is zero-sum and symmetric in each group By Satoh, Atsuhiro; Tanaka, Yasuhito
  2. On zero-sum game formulation of non zero-sum game By Satoh, Atsuhiro; Tanaka, Yasuhito
  3. Giving to Varying Numbers of Others By Matthew Robson; John Bone
  4. Nash equilibrium in asymmetric multi-players zero-sum game with two strategic variables and only one alien By Satoh, Atsuhiro; Tanaka, Yasuhito
  5. Sion's mini-max theorem and Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group By Atsuhiro Satoh; Yasuhito Tanaka
  6. Experimental Research on Contests By Roman Sheremeta
  7. Random Assignment of Bundles By Chatterji, Shurojit; Liu, Peng
  8. Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies By Anuj Bhowmik; Maria Gabriella Graziano
  9. Cooperative game-theoretic features of cost sharing in location-routing By Osicka, Ondrej; Guajardo, Mario; van Oost, Thibault
  10. Frugals, Militants and the Oil Market By Billette de Villemeur, Etienne; Pineau, Pierre-Olivier
  11. Contests with a Non-Convex Strategy Space By Doron Klunover; John Morgan
  12. Blocking in a timing game with asymmetric players By Smirnov, Vladimir; Wait, Andrew
  13. On Poverty and the International Allocation of Development Aid By Victor Ginsburgh; Juan D. Moreno-Ternero
  14. Placement Optimization in Refugee Resettlement By Trapp , Andrew C.; Teytelboym , Alexander; Martinello, Alessandro; Andersson, Tommy; Ahani, Narges
  15. Analyzing the Economics of Renewable Jet Fuels Using a Game-theoretic Approach By Sharma, Bijay P.; Yu, Tun-Hsiang Edward; English, Burton C.; Boyer, Christopher M.
  17. Strategic Voting when Participation is Costly By Dimitrios Xefteris
  18. Spin Doctors: A Model and an Experimental Investigation of Vague Disclosure By Marvin Deversi; Alessandro Ispano; Peter Schwardmann
  19. Crowdfunding in a duopoly under asymmetric information By Miglo, Anton
  20. General stopping behaviors of naïve and non-committed sophisticated agents, with application to probability distortion By Yu-Jui Huang; Adrien Nguyen-Huu; Xun Yu Zhou
  21. Mergers in Nonrenewable Resource Oligopolies and Environmental Policies By Ray Chaudhuri, A.; Benchekroun, H.; Breton, Michele
  22. Market Power in the Dairy Alternative Beverage Industry in the United States By Yang, Tingyi; Dharmasena, Senarath
  23. Factors for the formation of inefficient states when using tax incentive regimes By Sokolovskyi, Dmytro

  1. By: Satoh, Atsuhiro; Tanaka, Yasuhito
    Abstract: We consider the relation between Sion's minimax theorem for a continuous function and Nash equilibrium in a multi-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The existence of Nash equilibrium which is symmetric in each group implies a modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy for players in each group. %given the values of the strategic variables. 2. A modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy for players in each group implies the existence of Nash equilibrium which is symmetric in each group. Thus, they are equivalent. An example of such a game is a relative profit maximization game in each group under oligopoly with two groups such that firms in each group have the same cost functions and maximize their relative profits in each group, and the demand functions are symmetric for the firms in each group.
    Keywords: multi-players zero-sum game, two groups, Nash equilibrium, Sion's minimax theorem
    JEL: C72
    Date: 2018–09–13
  2. By: Satoh, Atsuhiro; Tanaka, Yasuhito
    Abstract: We consider a formulation of a non zero-sum n players game by an n+1 players zero-sum game. We suppose the existence of the n+1-th player in addition to n players in the main game, and virtual subsidies to the n players which is provided by the n+1-th player. Its strategic variable affects only the subsidies, and does not affect choice of strategies by the n players in the main game. His objective function is the opposite of the sum of the payoffs of the n players. We will show 1) The minimax theorem by Sion (Sion(1958)) implies the existence of Nash equilibrium in the n players non zero-sum game. 2) The maximin strategy of each player in {1, 2, ..., n} with the minimax strategy of the n+1-th player is equivalent to the Nash equilibrium strategy of the n players non zero-sum game. 3) The existence of Nash equilibrium in the n players non zero-sum game implies Sion's minimax theorem for pairs of each of the n players and the n+1-th player.
    Keywords: zero-sum game, non zero-sum game, minimax theorem, virtual subsidy
    JEL: C72
    Date: 2018–09–13
  3. By: Matthew Robson; John Bone
    Abstract: Within a modified N person dictator game, we test the extent to which giving behaviour changes as the number of recipients varies. Using a within-subject design, in an incentivised laboratory experiment, individual-level preference parameters are estimated within five alternative utility functions. Both goodness-of-fit and predictive accuracy of each model are analysed, with the "best" model identified for each individual. The Dirichlet distribution is proposed as a random behavioural model to rationalise noise; with parameters accounting for differential error arising from the complexity of decision problems. Results show that, on average, participants are willing to give more total payoffs to others as the number of players increase, but not maintain average payoffs to others. Extensive heterogeneity is found in individual preferences, with no model "best" fitting all individuals.
    Keywords: Distributional Preferences, Prosocial Behaviour, Group Size, Experimental Economics, Altruism, Social Welfare Function.
    JEL: C72 C91 D63 D64 I31
    Date: 2018–10
  4. By: Satoh, Atsuhiro; Tanaka, Yasuhito
    Abstract: We consider a partially asymmetric multi-players zero-sum game with two strategic variables. All but one players have the same payoff functions, and one player (Player $n$) does not. Two strategic variables are t_i's and s_i's for each player i. Mainly we will show the following results. 1) The equilibrium when all players choose t_i's is equivalent to the equilibrium when all but one players choose t_i's and Player n chooses s_n as their strategic variables. 2) The equilibrium when all players choose s_i's is equivalent to the equilibrium when all but one players choose s_i's and Player n chooses t_n as their strategic variables. The equilibrium when all players choose t_i's and the equilibrium when all players choose s_i's are not equivalent although they are equivalent in a symmetric game in which all players have the same payoff functions.
    Keywords: partially asymmetric multi-players zero-sum game, Nash equilibrium, two strategic variables
    JEL: C72
    Date: 2018–09–13
  5. By: Atsuhiro Satoh; Yasuhito Tanaka
    Abstract: We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The existence of Nash equilibrium which is symmetric in each group implies Sion's minimax theorem for a pair of playes in each group. 2. Sion's minimax theorem for a pair of playes in each group imply the existence of a Nash equilibrium which is symmetric in each group. Thus, they are equivalent. An example of such a game is a relative profit maximization game in each group under oligopoly with two groups such that firms in each group have the same cost functions and maximize their relative profits in each group, and the demand functions are symmetric for the firms in each group.
    Date: 2018–09
  6. By: Roman Sheremeta (Weatherhead School of Management, Case Western Reserve University and Economic Science Institute, Chapman University)
    Abstract: Costly competitions between economic agents are modeled as contests. Researchers use laboratory experiments to study contests and test comparative static predictions of contest theory. Commonly, researchers find that participants’ efforts are significantly higher than predicted by the standard Nash equilibrium. Despite overbidding, most comparative static predictions, such as the incentive effect, the size effect, the discouragement effect and others are supported in the laboratory. In addition, experimental studies examine various contest structures, including dynamic contests (such as multi-stage races, wars of attrition, tug-of-wars), multi-dimensional contests (such as Colonel Blotto games), and contests between groups. This article provides a short review of such studies.
    Keywords: Contest; All-pay auction; Tournament; Dynamic Contest; Multi-battle Contest; Multidimensional Contest; Group Contest; Rent-seeking; Experiment; Overbidding; Over-dissipation; Incentive Effect; Size Effect; Discouragement Effect; Strategic Momentum
    JEL: C7 C9 D4 D7 D9 H4 J4 K4 L2 M5
    Date: 2018
  7. By: Chatterji, Shurojit (School of Economics, Singapore Management University); Liu, Peng (School of Economics, Singapore Management University)
    Abstract: We study the random assignments of bundles with no free disposal. The key difference between the setting with bundles and the setting with objects (see Bogomolnaia and Moulin (2001)) is one of feasibility. The implications of this difference are significant. First, the characterization of sd-efficient random assignments is fundamentally different. Second, a possibility result in the setting with objects fails in the setting with bundles. However, in the setting with bundles, we are able to identify a preference restriction, called essential monotonicity, under which the random serial dictatorship rule (extended to the setting with bundles) is equivalent to the probabilistic serial rule (extended to the setting with bundles). This equivalence implies the existence of a rule on this restricted domain satisfying sdefficiency, sd-strategy-proofness, and equal treatment of equals. Moreover, this rule selects only random assignments which can be decomposed as convex combinations of deterministic assignments.
    Keywords: Random assignments; bundles; decomposability; sd efficiency; sd-strategyproofness; equal treatment of equals
    JEL: C78 D71
    Date: 2018–09–12
  8. By: Anuj Bhowmik (Indira Gandhi Institute of Development); Maria Gabriella Graziano (Università di Napoli Federico II and CSEF)
    Abstract: This paper analyses two properties of the core in a two-period exchange economy under uncertainty: the veto power of arbitrary sized coalitions; and coalitional fairness of core allocations. We study these properties in relation to classical (static) and sequential (dynamic) core notions and apply our results to asset markets and asymmetric information models. We develop a formal setting where consumption sets have no lower bound and impose a series of general restrictions on the first period trades of each agent. All our results are applications of the same lemma about improvements to an allocation that is either non-core or non-coalitionally fair. Roughly speaking, the lemma states that if all the members of a coalition achieve a better allocation in some way (for instance, by blocking the status quo allocation or because they envy the net trade of other coalitions) then an alternative improvement can be obtained through a perturbation of the initial improvement.
    Date: 2018–09–28
  9. By: Osicka, Ondrej (Dept. of Business and Management Science, Norwegian School of Economics); Guajardo, Mario (Dept. of Business and Management Science, Norwegian School of Economics); van Oost, Thibault (Louvain School of Management, Université catholique de Louvain)
    Abstract: This article studies several variants of the location-routing problem using a cooperative game-theoretic framework. The authors derive characteristics in terms of subadditivity, convexity, and non-emptiness of the core. Moreover, for some of the game variants, it is shown that for facility opening costs substantially larger than the costs associated with routing, the core is always non-empty. The theoretical results are supported by numerical experiments aimed at illustrating the properties and deriving insights. Among others, it is observed that, while in general it is not possible to guarantee core allocations, in a huge majority of cases the core is non-empty.
    Keywords: Collaborative logistics; Location-routing; Cooperative game theory; Cost allocation
    JEL: C00 C71
    Date: 2018–09–24
  10. By: Billette de Villemeur, Etienne; Pineau, Pierre-Olivier
    Abstract: The oil market has often been modelled as an oligopoly where the strategic players are producers. With climate change, a new sort of game appeared, where environmental militants play a significant role by opposing some projects, to contain oil production. At the same time, consumers continue to use increasing amounts of oil, independently of oil price fluctuations. Should we oppose oil project, reduce demand or both? We investigate in this paper the double prisoner's dilemma in which individuals find themselves, with respect to oil consumption and their environmental stance towards the oil industry. We find that the collective outcome of such game is clearly better when a frugal behaviour is adopted, without being militant. The Nash equilibrium, resulting from the individual strategies, leads by contrast to the worst possible outcome: high prices, high consumption and high environmental impact. An effective environmental action should avoid opposing oil supply sources (a costly militant act) and help consumers becoming more frugal.
    Keywords: Oil Market, Militants, Frugality
    JEL: D01 D7 Q41
    Date: 2018–08–01
  11. By: Doron Klunover; John Morgan
    Abstract: We characterize the Nash equilibria of a class of two-player contests with a non-convex strategy space under the usual concavity assumptions. The analysis sheds light on behavior in international conflicts. For instance, it may explain why some attempts to resolve international conflicts have been successful while others have not.
    Date: 2018–09
  12. By: Smirnov, Vladimir; Wait, Andrew
    Abstract: We examine innovation as a market-entry timing game with complete information and observable actions. We allow for heterogenous payoffs between players, and for a leader's payoff functions to be multi-peaked and non-monotonic. Assuming that the follower's payoff is non-increasing with the time of the leader's entry, we characterize all pure-strategy subgame perfect equilibria for the two-player asymmetric model, showing that there are at most two equilibria. Firm heterogeneity allows for equilibria with different characteristics than previously examined in the literature. For example, a fi rm may wish to enter earlier blocking its rival's entry, so as to avoid an anticipated lower future payoff if it waited. A notable feature of this blocking equilibrium is that rents need not be equalized between the leader and follower. We also show that if the followers' payoffs are non-monotonic, the iterative incentives to block each other's product launch may lead to starkly inefficient early entry in a continuous version of the centipede game.
    Keywords: timing games; blocking entry; innovation.
    Date: 2018–09
  13. By: Victor Ginsburgh; Juan D. Moreno-Ternero
    Abstract: We analyze the role of poverty levels in the allocation of international development aid. We estimate “claims” for each recipient, based on the incidence and depth of poverty in its territory, and explore possible reallocations of the current (overall) official development assistance (ODA) based on those claims. We consider four allocation rules rooted in ancient sources: the Aristotelian proportional rule, two constrained egalitarian rules, inspired by Maimonides, and the Talmud rule. Each of them is grounded on different normative principles, which allows us to assess the recipients’ claims in different ways. Our results indicate that the current allocation of international development aid cannot be supported by any of those rules, which makes us conclude that the allocation of ODA is not truly driven by the goal of eradicating world’s poverty.
    Keywords: Poverty; Development; Aid; Resource Allocation; Claims
    Date: 2018–09
  14. By: Trapp , Andrew C. (Foisie Business School, Worcester Polytechnic Institute); Teytelboym , Alexander (Department of Economics, University of Oxford); Martinello, Alessandro (Department of Economics, Lund University); Andersson, Tommy (Department of Economics, Lund University); Ahani, Narges (Foisie Business School, Worcester Polytechnic Institute)
    Abstract: The paper will be available on Wednesday October 3 at 9am (Swedish time)
    Keywords: Refugee Resettlement; Matching; Integer Optimization; Machine Learning; Humanitarian Operations
    JEL: C44 C61 C78 F22 J61
    Date: 2018–10–03
  15. By: Sharma, Bijay P.; Yu, Tun-Hsiang Edward; English, Burton C.; Boyer, Christopher M.
    Keywords: Agribusiness Economics and Management, Industrial Org./Supply Chain Management, Resource and Environmental Policy Analysis
    Date: 2018–06–20
  16. By: Benito Amaro, I.
    Abstract: This paper presents a theoretical model to analyze the incentives for protecting soil productivity in presence of separation of property and control in agricultural land. Using a dynamic model of contracts between the landlords and operators we analyze the incentives of different type of contracts (fixed rate contracts or sharecropping contracts) and their potential impact on soil conservation. The main research question of this paper is: do landlords and tenants have conflicting incentives regarding soil conservation? Our theoretical results are consistent with previous empirical literature that find that, depending on the contract specifications, there are no conflicting incentives.
    Keywords: Agricultural and Food Policy, Land Economics/Use
    Date: 2018–07
  17. By: Dimitrios Xefteris
    Abstract: We study a general multiparty model of plurality rule elections with costly participation, and prove that strategic voting -that is, situations in which some voters abandon their most preferred alternative and vote strategically for the serious contender they like most- may emerge in equilibrium; just like when participation is costless/compulsory (Palfrey, 1988). This is contrary to recent claims that strategic voting cannot occur when participation is costly (e.g. Arzumanyan and Polborn, 2017) and establishes that the Duverger’s psychological effect is present in a much larger set of cases than currently believed.
    Keywords: Multiparty elections; plurality rule; costly voting; Duverger’s law; strategic voting
    JEL: D71 D72
    Date: 2018–09
  18. By: Marvin Deversi; Alessandro Ispano; Peter Schwardmann
    Abstract: Unfavorable news are often delivered under the disguise of vagueness. But are people sufficiently naive to be fooled by such positive spin? We use a theoretical model and a laboratory experiment to study the strategic use of vagueness in a voluntary disclosure game. Consider a sender who aims at inflating a receiver’s estimate of her type and who may disclose any interval that contains her actual type. Theory predicts that when facing a possibly naive receiver, the sender discloses an interval that separates her from worse types but is upwardly vague. Senders in the experiment adopt this strategy and some (naive) receivers are systematically misled by it. Imposing precise disclosure leads to less, but more easily interpretable, disclosure. Both theory and experimental data further suggest that imposing precision improves overall information transmission and is especially beneficial to naive receivers. Our results have implications for the rules that govern the disclosure of quality-relevant information by firms, the disclosure of research findings by scientists, and testimonies in a court of law.
    Keywords: communication, naivete, flexibility, regulation
    JEL: D82 D83 C92 L15 D04
    Date: 2018
  19. By: Miglo, Anton
    Abstract: Traditionally crowdfunding has been used for funding very innovative projects. Recently, however, companies have begun using crowdfunding to finance more traditional products where they compete against other sellers of similar products. One of the major platforms Indiegogo launched several projects consistent with this trend. This paper offers a model of a duopoly where firms can use crowdfunding prior to direct sales. The model is based on asymmetric information between competitors regarding the demand for the product. It provides several implications that have not yet been tested. For example we find that high-demand firms can use crowdfunding to signal their quality.
    Keywords: crowdfunding, asymmetric information, reward-based crowdfunding, duopoly, signalling
    JEL: D43 D82 G32 L11 L13 L26 M13
    Date: 2018
  20. By: Yu-Jui Huang; Adrien Nguyen-Huu; Xun Yu Zhou
    Abstract: We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naıve agents who reoptimize continuously in time, as well as equilibrium strategies of sophisticated agents who anticipate but lack control over their future selves’ behaviors. When the state process is one dimensional and the payoff functional satisfies some regularity conditions, we prove that any equilibrium can be obtained as a fixed point of an operator. This operator represents strategic reasoning that takes the future selves’ behaviors into account. We then apply the general results to the case when the agents distort probability and the diffusion process is a geometric Brownian motion. The problem is inherently time-inconsistent as the level of distortion of a same event changes over time. We show how the strategic reasoning may turn a na¨ıve agent into a sophisticated one. Moreover, we derive stopping strategies of the two types of agent for various parameter specifications of the problem, illustrating rich behaviors beyond the extreme ones such as “neverstopping” or “never-starting".
    Keywords: optimal stopping, probability distortion, time inconsistency, naive and sophisticated agents, equilibrium stopping law
    JEL: G11 I12
    Date: 2018–09
  21. By: Ray Chaudhuri, A. (Tilburg University, Center For Economic Research); Benchekroun, H.; Breton, Michele
    Abstract: We examine the profitability of horizontal mergers within nonrenewable resource industries, which account for a large proportion of merger activities worldwide. Each firm owns a private stock of the resource and uses open-loop strategies when choosing its extraction path. We analytically show that even a small merger (merger of 2 firms) is always profitable when the resource stock owned by each firm is small enough. In the case where pollution is generated by the industry's activity, we show that an environmental policy that increases the firms' production cost or reduces their selling price can deter a merger. This speeds up the industry's extraction and thereby causes emissions to occur earlier than under a laissez-faire scenario.
    Keywords: exhaustible resources; horizontal mergers; environmental regulation; differential games
    JEL: Q39 L41 Q58
    Date: 2018
  22. By: Yang, Tingyi; Dharmasena, Senarath
    Abstract: Dairy alternative beverage market in the United States has been growing over the past decade. Although almond milk and soymilk are the fastest growing categories, there exist numerous other products such as coconut milk, rice milk, cashew nut milk, hazelnut milk, etc. There are well-known national brands as well as not-so-well-known private label and store brands that compete among dairy alternative beverages. These firms compete strategically for market share by differentiating their products by brand, price, advertising, promotion, positioning and merchandising. Using market level weekly purchase data from 2015 Nielsen scanner panel, price cost margins and market power of different brands is estimated assuming the presence of pure strategy Bertrand-Nash equilibrium in prices. Demand parameters are estimated using attribute space hedonic metric approach within the Barten synthetic demand model. Hedonic variables with regards to product attributes such as calorie, fat, protein, calcium and other nutrients are used to estimate demand elasticities using qualitative factor distances within the hedonic matrix of parameters associated with attributes. Preliminary analysis revealed own-price demand elasticities of soymilk, almond milk, and coconut milk at -1.13, -0.5, and 0.46. These are used to calculate price cost margins under various industry structures (such as in Nevo, 2000).
    Keywords: Industrial Organization, Marketing
    Date: 2018–01–17
  23. By: Sokolovskyi, Dmytro
    Abstract: The article investigates the problem of adopting the tax incentives regime in certain industries. The general problem of tax benefits is their ineffectiveness, which often leads to results contrary to expected and also to losses in economy. So this paper aimed to define the reasons, factors and loss prevention of failures related to implementing the tax incentives regime. In order to analyze the subject area, we use the object and process modeling of it. Particularly, we use the optimization models and game-theory tools. We classified the types of tax incentives regimes in order to distinguish two targets for implementation of tax benefits: increase the government revenue and diversification the product line; and also three strategies of granting tax exemptions: overall, targeted, and individual tax incentives. We found that the strategy of granting overall tax exemptions potentially can lead to “free-rider problem”, and strategy of granting the targeted and individual ones can create conditions for arising of adverse selection mechanism. We defined the conditions leading to increase the tax revenues in process of adopting the tax incentives regime. Also the analysis of “principal-agent” model as Nash equilibrium allowed to find the conditions of arising the ineffective norm of interaction between government and investor, when the first satisfies the investor’s unjustified claim related to obtaining tax incentives. Obtained patterns, despite of their non-numerical character, can be useful in business decision-making, because the revealed ineffective norms and states define concrete threats, which should be considered by policymakers in the process of adopting the tax incentives regime. The future research can be related to extension of formalization of mechanisms of granting tax exemptions and of arising the inefficient states and norms of agents’ behavior; to development of mechanisms of prevention of inefficient states in the process of implementation of tax incentives regimes; to investigate their concrete evidence in the process of adopting the tax incentives regime in actual practice.
    Keywords: tax incentive regimes; tax behavior of government; economic behavior of investors; free rider problem; adverse selection, “principal – agent” model
    JEL: C02 G02 H25
    Date: 2018–09–23

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