nep-gth New Economics Papers
on Game Theory
Issue of 2019‒07‒29
eighteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Necessary and sufficient condition for equilibrium of the Hotelling model By Satoshi Hayashi; Naoki Tsuge
  2. A Model of Weighted Network Formation By Baumann, L.
  3. Price Competition in a Vertizontally Differentiated Duopoly By Bos, Iwan; Peeters, Ronald
  4. Weighted nucleoli and dually essential coalitions (extended version) By Tamás Solymosi
  5. Rationalizability, Observability and Common Knowledge By Antonio Penta; Peio Zuazo-Garin
  6. Strategic complexity and the value of thinking By Gill, David; Prowse, Victoria
  7. Poisson voting games: proportional rule By Francesco De Sinopoli; Claudia Meroni
  8. Singularities and Catastrophes in Economics: Historical Perspectives and Future Directions By Michael S. Harr\'e; Adam Harris; Scott McCallum
  9. A class of globally solvable Markovian quadratic BSDE systems and applications By Xing, Hao; Žitković, Gordan
  10. The Institutional Dynamics of Colonial Exploitation By D'Alessandro, Simone; DISTEFANO, Tiziano
  11. On the Interaction between Small Decay, Agent Heterogeneity and Diameter of Minimal Strict Nash Networks in Two-way Flow Model: A Note By Charoensook, Banchongsan
  12. Adoption Gaps of Environmental Adaptation Technologies with Public Effects By Angelo Antoci; Simone Borghesi; Giulio Galdi; Sergio Vergalli
  13. Switching queues, cultural conventions, and social welfare By Stark, Oded; Budzinski, Wiktor; Kosiorowski, Grzegorz
  14. The Stability of Multi-Level Governments By Enriqueta Aragonès; Clara Ponsatí
  15. Natural resources and environment preservation: Strategic substitutability vs. complementarity in global and local public good provision By Acocella, Nicola; Di Bartolomeo, Giovanni
  16. Experimentation in Dynamic R&D Competition By Dosis, Anastasios; Muthoo, Abhinay
  17. Pledges as a Social Influence Device: Experimental Evidence By Damien Besancenot; Radu Vranceanu
  18. Pathways to Good Healthcare Services and Patient Satisfaction: An Evolutionary Game Theoretical Approach By Zainab Alalawi; The Anh Han; Yifeng Zeng; Aiman Elragig

  1. By: Satoshi Hayashi; Naoki Tsuge
    Abstract: We study a model of vendors competing to sell a homogeneous product to customers spread evenly along a linear city. This model is based on Hotelling's celebrated paper in 1929. Our aim in this paper is to present a necessary and sufficient condition for the equilibrium. This yields a representation for the equilibrium. To achieve this, we first formulate the model mathematically. Next, we prove that the condition holds if and only if vendors are equilibrium.
    Date: 2019–07
  2. By: Baumann, L.
    Abstract: The paper proposes a game of weighted network formation in which each agent has a limited resource to form links of possibly different intensities with other agents and to use for private purposes. We show that every equilibrium is either “reciprocal” or “non-reciprocal”. In a reciprocal equilibrium, any two agents invest equally in the link between them. In a non-reciprocal equilibrium, agents are partitioned into “concentrated” and “diversified” agents and a concentrated agent is only linked to diversified agents and vice versa. For every link, the concentrated agent invests more in the link than the diversified agent. The unweighted relationship graph of an equilibrium, in which two agents are linked if they both invest positively in each other, uniquely predicts the equilibrium values of each agent's network investment and utility level, as well as the ratio of any two agents' investments in each other. We show that equilibria are not pairwise stable and not efficient due to the positive externalities of investing in a link.
    Keywords: weighted networks, network formation, link-specific investment
    JEL: D85 L14 Z13 C72
    Date: 2019–07–01
  3. By: Bos, Iwan (Organisation and Strategy); Peeters, Ronald (university of otago, dunedin)
    Abstract: This paper analyzes price competition in a duopoly market in which products are both horizontally and vertically differentiated. Firms offer a basic and a premium product to buyers, some of whom are brand loyal. We establish the existence of a unique and symmetric Nash pricing equilibrium. Equilibrium prices are increasing in the degree of horizontal differentiation and the amount of brand loyal customers. The equilibrium price of the basic (premium) good is decreasing (increasing) in the quality difference and profits can increase in costs when this difference is high enough. If the pricing decision is taken at the product (division) level, then there is again a unique (and symmetric) Nash equilibrium. Equilibrium prices and profits are lower than in the centralized case and demand for the basic product is higher when the quality difference is sufficiently large. Welfare is unambiguously lower with decentralized pricing.
    Keywords: vertizontal differentiation, pricing, multiproduct oligopoly
    JEL: D43 L13
    Date: 2019–06–20
  4. By: Tamás Solymosi (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest)
    Abstract: We study linearly weighted versions of the least core and the (pre)nucleolus and investigate the reduction possibilities in their computation. We slightly extend some well-known related results and establish their counterparts by using the dual game. Our main results imply, for example, that if the core of the game is not empty, all dually inessential coalitions (which can be weakly minorized by a partition in the dual game) can be ignored when we compute the per-capita least core and the per-capita (pre)nucleolus from the dual game. This could lead to the design of polynomial time algorithms for the per-capita (and other monotone nondecreasingly weighted versions of the) least core and the (pre)nucleolus in specific classes of balanced games with polynomial many dually essential coalitions.
    Keywords: nucleolus, least core, weighted nucleoli, efficient computation, cooperative game
    JEL: C71
    Date: 2019–05
  5. By: Antonio Penta; Peio Zuazo-Garin
    Abstract: We study the strategic impact of players' higher order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect information. Over this space, we characterize the correspondence of a solution concept which represents the behavioral implications of Rationality and Common Belief in Rationality (RCBR), where `rationality' is understood as sequential whenever a player moves second. We show that such a correspondence is generically single-valued, and that its structure supports a robust refinement of rationalizability, which often has very sharp implications. For instance: (i) in a class of games which includes both zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium, RCBR generically ensures efficient equilibrium outcomes; (ii) in a class of games which also includes other well-known families of coordination games, RCBR generically selects components of the Stackelberg pro les; (iii) if common knowledge is maintained that player 2's action is not observable (e.g., because 1 is commonly known to move earlier, etc.), in a class of games which includes of all the above RCBR generically selects the equilibrium of the static game most favorable to player 1.
    Keywords: eductive coordination, extensive form uncertainty, first-mover advantage, Krpes hypothesis, higher order beliefs, Rationalizability, robustness, Stackelberg selections
    JEL: C70 C71 C72 D82 D83
    Date: 2019–07
  6. By: Gill, David (Purdue University); Prowse, Victoria (Purdue University)
    Abstract: Response times are a simple low-cost indicator of the process of reasoning in strategic games. In this paper, we leverage the dynamic nature of response-time data from repeated strategic interactions to measure the strategic complexity of a situation by how long people think on average whenthey face that situation (where we categorize situations according to the characteristics of play in the previous round). We find that strategic complexity varies significantly across situations, and we find considerable heterogeneity in how responsive subjects’ thinking times are to complexity. We also study how variation in response times at the individual level across rounds affects strategic behavior and success. We find that ‘overthinking’ is detrimental to performance: when a subject thinks for longer than she would normally do in a particular situation, she wins less frequently and earns less. The behavioral mechanism that drives the reduction in performance is a tendency to move away from Nash equilibrium behavior. Overthinking is detrimental even though subjects who think for longer on average tend to be more successful. Finally, cognitive ability and personality have no effect on average response times.
    Keywords: Response time; decision time; thinking time; strategic complexity; game theory; strategic games; repeated games; beauty contest; cognitive ability; personality. JEL Classification: C72; C91.
    Date: 2019
  7. By: Francesco De Sinopoli (Department of Economics (University of Verona)); Claudia Meroni (Department of Economics (University of Verona))
    Abstract: We analyze strategic voting under pure proportional rule and two candidates, embedding the basic spatial model into the Poisson framework of population uncertainty. We prove that the Nash equilibrium exists and is unique. We show that it is characterized by a cutpoint in the policy space that is always located between the mean of the two candidates’ positions and the median of the distribution of voters’ types. We also show that, as the expected number of voters goes to infinity, the equilibrium converges to that of the complete information case.
    Keywords: Poisson games, strategic voting, proportional rule
    JEL: C72 D72
    Date: 2019–07
  8. By: Michael S. Harr\'e; Adam Harris; Scott McCallum
    Abstract: Economic theory is a mathematically rich field in which there are opportunities for the formal analysis of singularities and catastrophes. This article looks at the historical context of singularities through the work of two eminent Frenchmen around the late 1960s and 1970s. Ren\'e Thom (1923-2002) was an acclaimed mathematician having received the Fields Medal in 1958, whereas G\'erard Debreu (1921-2004) would receive the Nobel Prize in economics in 1983. Both were highly influential within their fields and given the fundamental nature of their work, the potential for cross-fertilisation would seem to be quite promising. This was not to be the case: Debreu knew of Thom's work and cited it in the analysis of his own work, but despite this and other applied mathematicians taking catastrophe theory to economics, the theory never achieved a lasting following and relatively few results were published. This article reviews Debreu's analysis of the so called ${\it regular}$ and ${\it crtitical}$ economies in order to draw some insights into the economic perspective of singularities before moving to how singularities arise naturally in the Nash equilibria of game theory. Finally a modern treatment of stochastic game theory is covered through recent work on the quantal response equilibrium. In this view the Nash equilibrium is to the quantal response equilibrium what deterministic catastrophe theory is to stochastic catastrophe theory, with some caveats regarding when this analogy breaks down discussed at the end.
    Date: 2019–07
  9. By: Xing, Hao; Žitković, Gordan
    Abstract: We establish global existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the generator, an a-priori local-boundedness property, and a locally-Hölder-continuous terminal condition. We present easily verifiable sufficient conditions for these assumptions and treat several applications, including stochastic equilibria in incomplete financial markets, stochastic differential games, and martingales on Riemannian manifolds
    Keywords: BSDE; backward stochastic differential equations; systems of BSDE; quadratic nonlinearities; stochastic equilibrium; martingales on manifolds; nonzero-sum stochastic games
    JEL: C1
    Date: 2018–02–05
  10. By: D'Alessandro, Simone; DISTEFANO, Tiziano
    Abstract: This paper focuses on the interaction between the legacy of institutional arrangements and incentives on long-term development. We recalled two studies focusing on the long term effects of geographic discontinuities in colonial practice in India and Peru and we confronted the two historical cases as to emphasise the role of capital accumulation and equality of distribution. Furthermore, we propose an evolutionary game model to capture the evolutionary dynamics of institutional assets defining egalitarian or iniquitous income divisions in a non-cooperative setting. This framework sheds light on the role of the colonial governments in the interaction between local institutions and foreign colonial rule in terms of distribution, resources extraction, social asymmetries and finalised investments.
    Keywords: Colonialism, Evolutionary Game Theory, Solow growth theory, inequality
    JEL: F43 O1 P3
    Date: 2019–07–01
  11. By: Charoensook, Banchongsan
    Abstract: In this note, I study the roles of value heterogeneity - i.e., agents are heterogeneous in terms of values of nonrival information thay they possessed - in determining the shapes of two-way flow Strict Nash networks when small amount of decay is present. I do so by extending the two-way flow network with small decay of De Jaegher and Kamphorst (J ECON BEHAV ORGAN, 2015). Results of this extension shows that the effects of value heterogeneity on Strict Nash networks, when small decay is present, largely resemble the effects of heterogeneity in link formation cost - without decay - found in the literature. Another surprising finding is that value heterogeneity can extend the diameters of Strict Nash networks without changing any other properties. In the discussion section of this note, I relate this finding to two well-known concepts in the studies of social networks - small world and preferential attachment.
    Keywords: Research Methods/ Statistical Methods
    Date: 2019–07–24
  12. By: Angelo Antoci (University of Sassari); Simone Borghesi (University of Siena and European University Institute); Giulio Galdi (University of Siena); Sergio Vergalli (Fondazione Eni Enrico Mattei and University of Brescia)
    Abstract: The global nature of the climatic challenge requires a high level of cooperation among agents, especially since most of the related coping strategies produce some kind of externalities toward others. Whether they are positive or negative, the presence of externalities may lead the system towards Pareto-dominated states. In this work, we study under and over-adoption of environmental adaptation technologies which enhance environmental quality for the individual while transferring externalities to other agents. We distinguish adaptation technologies between maladaptation and mitigation ones, depending on the sign of the externalities. In particular, we show that over adoption may occur for maladaptive technologies, whereas under-adoption may occur in case of mitigation. We study a model with two regions at different stages of development, which allows us to draw considerations on well-being consequences of environmental dumping.
    Keywords: Adaptation, Negative Externalities, Evolutionary Dynamics, Public Good Game, Environmental Dumping
    JEL: C70 D62 O13 O40 Q20
    Date: 2019–07
  13. By: Stark, Oded; Budzinski, Wiktor; Kosiorowski, Grzegorz
    Abstract: We use queuing-related behavior as an instrument for assessing the social appeal of alternative cultural norms. Specifically, we study the behavior of rational and sophisticated individuals who stand in a given queue waiting to be served, and who, in order to speed up the process, consider switching to another queue. We look at two regimes that govern the possible order in which the individuals stand should they switch to the other queue: a regime in which cultural convention, social norms, and basic notions of fairness require that the order in the initial queue is preserved, and a regime without such cultural inhibitions, in which case the order in the other queue is random, with each configuration or sequence being equally likely. We seek to find out whether in these two regimes the aggregate of the behaviors of self-interested individuals adds up to the social optimum defined as the shortest possible total waiting time. To do this, we draw on a Nash Equilibrium setting. We find that in the case of the preserved order, the equilibrium outcomes are always socially optimal. However, in the case of the random order, unless the number of individuals is small, the equilibrium outcomes are not socially optimal.
    Keywords: Decision processes,Queuing,Nash Equilibrium,Social customs,Social welfare
    JEL: C72 D60 Z13
    Date: 2019
  14. By: Enriqueta Aragonès; Clara Ponsatí
    Abstract: This paper studies the stability of a multi-level government. We analyze an extensive form game played between two politicians leading two levels of government. We characterize the conditions that render such government structures stable. We also show that if leaders care about electoral rents and the preferences of the constituencies at different levels are misaligned, then the decentralized government structure may be unsustainable. This result is puzzling because, from a normative perspective, the optimality of decentralized decisions via a multi-level government structure is relevant precisely when different territorial constituencies exhibit preference heterogeneity.
    Keywords: multi-level governments, repression
    JEL: D72
    Date: 2019–07
  15. By: Acocella, Nicola; Di Bartolomeo, Giovanni
    Abstract: Environment is a public good whose preservation requires some type of intervention. Use of natural resources for economic activities should be regulated by the local communities; however, this can have in turn external effects on other communities. Environment then takes the double nature of local and global public good, requiring intervention of different levels of governments, whose interplay may raise further conflicts. The aim of this paper is twofold. First, we survey the literature on conflicts arising from the alternative uses of land and natural resources and discuss the effects and policy implications of the interplay between different governments. Second, we focus on the role of strategic interactions in the environmental governance and the implied policy trade-offs and present a formal policy game with potential conflicts between central and local authorities. The model aims to describe the circumstances according to which the lack of coordination between local and central authorities leads to under- or over- provision of natural resources and environment preservation.
    Keywords: Environment,Development,Public goods,Conflict
    Date: 2019
  16. By: Dosis, Anastasios (ESSEC Business School and THEMA); Muthoo, Abhinay (University of Warwick)
    Abstract: We study a two-stage, winner-takes-all, R&D race, in which, at the outset, firms are uncertain regarding the viability of the project. Learning through experimentation introduces a bilateral (dynamic) feedback mechanism. For relatively low-value products,the equilibrium stopping time coincides with the socially efficient stopping time although firms might experiment excessively inequilibrium; forrelatively high-value products, firms might reduce experimentation and stop rather prematurely due to the fundamental free-riding effect. Perhaps surprisingly, a decrease in the value of the product can spur experimentation.
    Keywords: Experimentation ; learning ; dynamic R&D competition ; inefficiency
    JEL: C73 D83 O31 O32
    Date: 2019
  17. By: Damien Besancenot (LIRAES - EA 4470 - Laboratoire Interdisciplinaire de Recherche Appliquée en Economie de la Santé - UPD5 - Université Paris Descartes - Paris 5, UPD5 - Université Paris Descartes - Paris 5); Radu Vranceanu (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique, ESSEC Business School - Essec Business School)
    Abstract: This paper reports the results from a two-person "pledge and give" experiment. Each person's endowment is private information available only to him. In the first stage, each agent informs the other about the amount he intends to give, or makes a pledge. In the second stage, each agent makes a contribution to the joint donation. A simple theoretical model shows that in this game the equilibrium pledge function is linear in the endowment of each agent. Furthermore, if agents have a strong taste for conformity, the optimal gift is positively related to one's own endowment and to the pledge of his partner. Data from the lab experiment show that, indeed, subjects pledge approximately 60% of their endowment. Also, pledges have an important social influence role: an agent will increase his donation by 20 cents on average if his partner pledges one more euro.
    Keywords: charity giving,conformity,strategic pledges,social influence
    Date: 2019–06–24
  18. By: Zainab Alalawi; The Anh Han; Yifeng Zeng; Aiman Elragig
    Abstract: Spending by the UK's National Health Service (NHS) on independent healthcare treatment has been increased in recent years and is predicted to sustain its upward trend with the forecast of population growth. Some have viewed this increase as an attempt not to expand the patients' choices but to privatize public healthcare. This debate poses a social dilemma whether the NHS should stop cooperating with Private providers. This paper contributes to healthcare economic modelling by investigating the evolution of cooperation among three proposed populations: Public Healthcare Providers, Private Healthcare Providers and Patients. The Patient population is included as a main player in the decision-making process by expanding patient's choices of treatment. We develop a generic basic model that measures the cost of healthcare provision based on given parameters, such as NHS and private healthcare providers' cost of investments in both sectors, cost of treatments and gained benefits. A patient's costly punishment is introduced as a mechanism to enhance cooperation among the three populations. Our findings show that cooperation can be improved with the introduction of punishment (patient's punishment) against defecting providers. Although punishment increases cooperation, it is very costly considering the small improvement in cooperation in comparison to the basic model.
    Date: 2019–07

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