nep-gth New Economics Papers
on Game Theory
Issue of 2019‒09‒16
sixteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Renegotiation and Coordination with Private Values By Yuval Heller; Christoph Kuzmics
  2. Nash Equilibria in Optimal Reinsurance Bargaining By Michail Anthropelos; Tim J. Boonen
  3. A fixed-point policy-iteration-type algorithm for symmetric nonzero-sum stochastic impulse games By Diego Zabaljauregui
  4. The Cowles Commission and Foundation for Research in Economics: Bringing Mathematical Economics and Econometrics from the Fringes of Economics to the Mainstream By Robert W. Dimand
  5. Decision Making and Games with Vector Outcomes By Silvia Albrizio
  6. Linear Equilibria for Dynamic LQG Games with Asymmetric Information and Dependent Types By Nasimeh Heydaribeni; Achilleas Anastasopoulos
  7. General Competing Mechanisms with Frictions By Seungjin Han
  8. Production Substitution of Goods Within and Between Firms in a Multiproduct Duopoly By Tetsuya Shinkai; Ryoma Kitamura
  9. Explicit Solution Algorithms for Order and Price Postponement in Multi-periodic Channel Optimization By Azad Gholami, Reza; Sandal, Leif K.; Ubøe, Jan
  10. Ambitious Emissions Goal as a Strategic Preemption By Hiroaki Yamagami; Ryo Arawatari; Takeo Hori
  11. Conflict Between Riparian Countries By Yousef, Sahar
  12. The Credit Cycle and the Financial Fragility Hypothesis: An Evolutionary Population Approach By JORGE OMAR RAZO-DE ANDA; SALVADOR CRUZ-AKÉ; ANA CECILIA PARADA-ROJAS
  13. Solution Algorithms for Optimal Buy-Back Contracts in Multi-period Channel Equilibria with Stochastic Demand and Delayed Information By Azad Gholami, Reza; Sandal, Leif K.; Ubøe, Jan
  14. Modelling Cooperation in a Dynamic Healthcare System By Zainab Alalawi; Yifeng Zeng; The Anh Han; Aiman Elragig
  15. Timing of Government Intervention and the Multiple Equilibria of Currency Crisis By Young-Han Kim; Hanjoon Jung
  16. Climate Policy under Spatial Heat Transport: Cooperative and Noncooperative Regional Outcomes By Yongyang Cai; William Brock; Anastasios Xepapadeas; Kenneth Judd

  1. By: Yuval Heller (Bar Ilan University, Israel); Christoph Kuzmics (University of Graz, Austria)
    Abstract: We define and characterize renegotiation-proof equilibria of coordination games with preplay communication in which players have private preferences over the feasible coordinated outcomes. These are such that players never miscoordinate, players coordinate on their jointly preferred outcome whenever there is one, and players communicate only the ordinal part of their preferences. This set of renegotiation proof equilibrium strategies does not depend on the distribution of private preferences, and is thus robust to changes in players’ beliefs. Moreover, these equilibria are interim Pareto efficient and evolutionarily stable.
    Keywords: Coordination games; Renegotiation-proof; Equilibrium entrants; Secret handshake; Incomplete information; Evolutionary robustness
    JEL: C72 C73 D82
    Date: 2019–09
  2. By: Michail Anthropelos; Tim J. Boonen
    Abstract: We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents' strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents' bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.
    Date: 2019–09
  3. By: Diego Zabaljauregui
    Abstract: Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make strong assumptions pertaining very particular cases. To the author's best knowledge, the only numerical method in the literature is the heuristic one we put forward to solve an underlying system of quasi-variational inequalities. Focusing on symmetric games, this paper presents a simpler and more efficient fixed-point policy-iteration-type algorithm which removes the strong dependence on the initial guess and the relaxation scheme of the previous method. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. A provably convergent single-player impulse control solver, often outperforming classical policy iteration, is also provided. The main algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise too challenging problems, and even some for which results go beyond the scope of all the currently available theory.
    Date: 2019–09
  4. By: Robert W. Dimand (Department of Economics, Brock University)
    Abstract: Founded in 1932 by a newspaper heir disillusioned by the failure of forecasters to predict the Great Crash, the Cowles Commission promoted the use of formal mathematical and statistical methods in economics, initially through summer research conferences in Colorado and through support of the Econometric Society (of which Alfred Cowles was secretary-treasurer for decades). After moving to the University of Chicago in 1939, the Cowles Commission sponsored works, many later honored with Nobel Prizes but at the time out of the mainstream of economics, by Haavelmo, Hurwicz and Koopmans on econometrics, Arrow and Debreu on general equilibrium, Yntema and Mosak on general equilibrium in international trade theory, Arrow on social choice, Koopmans on activity analysis, Klein on macroeconometric modelling, Lange, Marschak and Patinkin on macroeconomic theory, and Markowitz on portfolio choice, but came into intense methodological, ideological and personal conflict with the emerging “Chicago school.” This conflict led the Cowles Commission to move to Yale in 1955 as the Cowles Foundation, directed by James Tobin (who had declined to move to Chicago to direct it). The Cowles Foundation remained a leader in the more technical areas of economics, notably with Tobin’s “Yale school” of monetary theory, Scarf’s computable general equilibrium, Shubik in game theory, and later Phillips and Andrews in econometric theory but as formal methods in economic theory and econometrics pervaded the discipline of economics, Cowles (like the Econometric Society) became less distinct from the rest of economics.
    Keywords: Cowles Commission, Formalism in economics, Mathematics in economics, Cowles approach to econometrics
    JEL: B23 B41 C01 C02
    Date: 2019–06
  5. By: Silvia Albrizio (Yonsei University)
    Abstract: In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization.
    Keywords: Decision making, Duality, Games, Incomplete preferences, Utility representation, Vector outcomes.
    JEL: C02 C72 D01
    Date: 2019–09
  6. By: Nasimeh Heydaribeni; Achilleas Anastasopoulos
    Abstract: We consider a non-zero-sum linear quadratic Gaussian (LQG) dynamic game with asymmetric information. Each player observes privately a noisy version of a (hidden) state of the world $V$, resulting in dependent private observations. We study perfect Bayesian equilibria (PBE) for this game with equilibrium strategies that are linear in players' private estimates of $V$. The main difficulty arises from the fact that players need to construct estimates on other players' estimate on $V$, which in turn would imply that an infinite hierarchy of estimates on estimates needs to be constructed, rendering the problem unsolvable. We show that this is not the case: each player's estimate on other players' estimates on $V$ can be summarized into her own estimate on $V$ and some appropriately defined public information. Based on this finding we characterize the PBE through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, Kalman filter covariance matrices, as well as some other required quantities, are observation-dependent and thus cannot be evaluated off-line through a forward recursion.
    Date: 2019–09
  7. By: Seungjin Han
    Abstract: This paper studies the class of robust equilibria in a general competing mechanism game for decentralized markets with frictions in which non-deviating sellers punish a deviator with dominant strategy incentive compatible (DIC) direct mechanisms. Given one-dimensional, independent, and private types, the lower bound of a seller's payoff in such equilibria is his minmax value over all DIC direct mechanisms if a seller can deviate to a contract that determines a menu of any complex mechanisms conditional on buyers' messages and he chooses a mechanism he wants from it. In applications, the number of sellers is endogenized given a number of buyers and fixed entry costs. As the number of buyer increases, a unique equilibrium emerges and the equilibrium ratio of buyers to sellers converges to the point where a seller's net profit is zero with the monopoly terms of trade.
    Keywords: competing mechanisms, dominant strategy incentive compatibility, frictions, implicit collusion
    JEL: C72 D82
    Date: 2019–09
  8. By: Tetsuya Shinkai (School of Economics, Kwansei Gakuin University); Ryoma Kitamura (Faculty of Economics, Otemon Gakuin University)
    Abstract: We consider the product line strategies of duopolistic firms, each of which can supply two vertically-differentiated products under nonnegative output constraints and expectations of their rival's product line reaction. Considering a game of firms with heterogeneous (homogeneous) unit costs for high- (low-) quality products, we derive the equilibria for the game and conduct comparative statics of the equilibria outcomes on the relative superiority of the high-quality product and relative cost efficiency. In two of the equilibria, we find that where the cost-inefficient firm supplies a high-quality good, social welfare can worsen as its unit cost decreases. We also characterize the result using the production substitution of differentiated goods within a firm and the high-quality good between firms. Further, by comparing social welfare in the first-best equilibria with those in the Cournot duopoly equilibria, we find that the social welfare of the market worsens in the multiproduct Cournot duopoly equilibria as the relative superiority of the high-quality good increases.
    Keywords: Multiproduct firm; Duopoly; Production substitution; Vertical product differentiation
    JEL: D21 D43 L13 L15
    Date: 2019–09
  9. By: Azad Gholami, Reza (Dept. of Business and Management Science, Norwegian School of Economics); Sandal, Leif K. (Dept. of Business and Management Science, Norwegian School of Economics); Ubøe, Jan (Dept. of Business and Management Science, Norwegian School of Economics)
    Abstract: Supply channels typically face uncertain and time-varying demand. Nonetheless, time-dependent channel optimization while addressing uncertain demand has received limited attention due to the high level of complexity of the ensuing nested equilibrium problems. The level of complexity rises when demand is dependent on current and previous prices. We consider a decentralized supply channel whose two members, a manufacturer and a retailer, must address the demand for a perishable commodity within a multi-period time horizon. Using a general (additive-multiplicative) stochastic model for the price-dependent demand, the purpose of this paper is to provide the channel members with analytic tools to devise optimal pricing and supply strategies at different times. In the first part of the paper, we propose a constructive theorem providing an explicit solution algorithm to obtain equilibrium states for bilevel optimization in decentralized supply channels. We also prove that the resulting equilibria are subgame perfect. In the second part, we allow the retailer to postpone her supply and pricing decisions until demand uncertainty is resolved at each period. Using subgame perfectness of the equilibria, we propose solution algorithms that use the extra information obtained by postponement. Finally, in a number of comparison theorems, we show that postponement strategies are always beneficial for a centralized channel (whose revenue structure is identical to that of a retailer). Whereas for a decentralized channel, due to vertical competitions, there may be scenarios wherein postponement strategies, i.e. access to extra information, turn out to be detrimental to the manufacturer and even to the whole channel.
    Keywords: Stochastic optimization; bilevel programming; game theory; pricing theory; stochastic demand; time-dependent demand; price-dependent demand
    JEL: C61 C73 D81
    Date: 2019–09–09
  10. By: Hiroaki Yamagami (Seikei University); Ryo Arawatari (Doshisha University); Takeo Hori (Tokyo Institute of Technology)
    Abstract: We model a political game where a policymaker pledges a domestic emissions goal in the context of instrument choice between carbon pricing (CP) and a quota approach. We show that, although the policymaker faces an emissions goal proposed from an international environmental agreement, she may pledge a more stringent emissions than the proposed level. We define this stringent goal as an “ambitious emissions goal". We show that the ambitious emissions goal acts as a strategy for the policymaker that preempts the industry's lobby in a subsequent stage. We also suppose that, if CP is introduced, a rent-seeking contest for the CP revenue refund is held. Then, if the contest is socially costly enough, CP is no longer an optimal instrument. Finally, we extend the model of one country to that of two symmetric countries. A Nash equilibrium where both countries pledge the ambitious emissions goals remains.
    Keywords: Lobby, Carbon pricing, Voluntary approach, Revenue refund, Rent-seeking
    JEL: D72 Q58
    Date: 2019–09
  11. By: Yousef, Sahar
    Keywords: Resource /Energy Economics and Policy
    Date: 2019–06–25
    Abstract: Minsky's idea of triggering a financial crisis is the adoption of risky financial positions by companies and their relationship with the financial system through banks and the credit they provide. The present work seeks to provide an explanation from a microeconomic point of view through the behavior of agents and their decision making under a Theory of evolutionary games, especially population games. The great advantage of this type of games is that it allows us to obtain proportions of the different decisions that a population or subpopulation is taking and how their interaction promotes equilibrium and the dynamics towards (or around) them.This allows us to determine the dynamics and equilibria of the credit cycle, following Minsky's idea of financial fragility. Additionally, the dynamics of the replicator allows transforming the differential equations in a Lotka-Volterra system, from which it can be concluded that both companies and banks adopt a predatory prey relationship in order to survive.
    Keywords: Capital Structure, Evolutionary Games, Behavioral Microeconomics
    JEL: G02 C73 G01
    Date: 2019–06
  13. By: Azad Gholami, Reza (Dept. of Business and Management Science, Norwegian School of Economics); Sandal, Leif K. (Dept. of Business and Management Science, Norwegian School of Economics); Ubøe, Jan (Dept. of Business and Management Science, Norwegian School of Economics)
    Abstract: We analyze the problem of time-dependent channel coordination in the face of uncertain demand. The channel, composed of a manufacturer and a retailer, is to address a time-varying and uncertain price-dependent demand. The decision variables of the manufacturer are wholesale and (possibly zero) buy-back prices, and those of the retailer are order quantity and retail price. Moreover, at each period, the retailer is allowed to postpone her retail price until demand uncertainty is resolved. In order to place emphasis on the price-decadent nature of demand, we embed a class of memory effects in demand structure, such that current demand at each period demand is affected by pricing history as well as current price. The ensuing equilibria problems, thus, become highly nested in time. We then propose our memory-based solution algorithm which coordinates the channel with optimal buy-back contracts at each period. We show that, contrary to the conventional belief, too generous buy-back prices may not only be suboptimal to the manufacturer, but also decrease the expected profit for the retailer and thus for the whole channel.
    Keywords: Stochastic optimization; bilevel programming; game theory; channel coordination; buy-back contracts; price postponement; pricing theory; contract theory
    JEL: C61 C73 D81
    Date: 2019–09–09
  14. By: Zainab Alalawi; Yifeng Zeng; The Anh Han; Aiman Elragig
    Abstract: Our research is concerned with studying behavioural changes within a dynamic system, i.e. health care, and their effects on the decision-making process. Evolutionary Game theory is applied to investigate the most probable strategy(ies) adopted by individuals in a finite population based on the interactions among them with an eye to modelling behaviour using the following metrics: cost of investment, cost of management, cost of treatment, reputation benefit for the provider(s), and the gained health benefit for the patient.
    Date: 2019–09
  15. By: Young-Han Kim (Sungkyunkwan University); Hanjoon Jung (Tianjin University)
    Abstract: This paper examines how currency crisis is affected by different timing of government intervention in the currency market. Since the seminal paper of Morris and Shin (1998), which shows that the self-fulfilling crisis can be avoided when noisy signals are considered, the conditions for the multiple equilibria have been widely studied. We contribute the studies by focusing on the timing of government intervention in the currency market. When the government intervenes in the market as a first mover, while speculators move as a second mover, the unique equilibrium of the currency market collapses since speculators can successfully coordinate after observing the government?s decisions. If the government moves as a second mover as in the case of Morris and Shin (1998), the unique equilibrium exists with noisy signals. When the government and speculators move simultaneously, there is no equilibrium with noisy information while there might be a unique equilibrium with perfect information. The results implicate that rash government intervention as a first mover might aggravate the currency crisis since the speculators have bigger opportunity for speculative coordination after observing the government?s action. The equilibria are also defined when the government intervention occurs in a repeated fashion, and the implications are discussed.
    Keywords: Currency crises, government intervention timing, multiple equilibria, unique equilibrium in currency regime
    JEL: F42 E61 P11
    Date: 2019–07
  16. By: Yongyang Cai; William Brock; Anastasios Xepapadeas; Kenneth Judd
    Abstract: We build a novel stochastic dynamic regional integrated assessment model (IAM) of the climate and economic system including a number of important climate science elements that are missing in most IAMs. These elements are spatial heat transport from the Equator to the Poles, sea level rise, permafrost thaw and tipping points. We study optimal policies under cooperation and noncooperation between two regions (the North and the Tropic-South) in the face of risks and recursive utility. We introduce a new general computational algorithm to find feedback Nash equilibrium. Our results suggest that when the elements of climate science are ignored, important policy variables such as the optimal regional carbon tax and adaptation could be seriously biased. We also find the regional carbon tax is significantly smaller in the feedback Nash equilibrium than in the social planner's problem in each region, and the North has higher carbon taxes than the Tropic-South.
    Date: 2019–09

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