nep-gth New Economics Papers
on Game Theory
Issue of 2009‒12‒19
nineteen papers chosen by
Laszlo A. Koczy
Budapest Tech and Maastricht University

  1. The Partnered Core of a Game with Side Payments By Philip J. Reny; Eyal Winter; Myrna Wooders
  2. Strongly Rational Sets for Normal-Form Games By Grandjean Gilles; Mauleon Ana; Vannetelbosch Vincent
  3. Sharing a Risky Cake By David R. Baqaee
  4. Nash Equilibrium Strategies in Discrete-Time Finite-Horizon Dynamic Games with Risk-and Effort-Averse Players By Dan Protopopescu
  5. Convexity and Complementarity in Network Formation: Implications for the Structure of Pairwise Stable Networks By Tim Hellmann
  6. Market Games and Clubs By Myrna Wooders
  7. On the Truly Noncooperative Game of Island Life: Introducing a Unified Theory of Value & Evolutionarily Stable Island Economic Development Strategy By Funk, Matt
  8. Dynamic Stackelberg Game with Risk-Averse Players: Optimal Risk-Sharing under Asymmetric Information By Dan Protopopescu
  9. Bayesian and Consistent Assessments By Carlos Pimienta
  10. Networks with decreasing returns to linking By Filippo Vergara Caffarelli
  11. Divisible-good uniform price auctions: the role of allocation rules and communication among bidders By Martin Sefton; Ping Zhang
  12. Communication, Coordination and Networks By Choi, Syngjoo; Lee, Jihong
  13. Networks and Markets: The dynamic impacts of information, matching and transaction costs on global trade By Yuki Kumagai
  14. Social Networks By De Martí, Joan; Zenou, Yves
  15. Two-way Flow Networks with Small Decay By Kris De Jaegher; Jurjen Kamphorst
  16. Ascending auctions: some impossibility results and their resolutions with final price discounts By Laurent Lamy
  17. Does category reporting increase donations to charity? A signalling game approach. By Edward Cartwright; Amrish Patel
  18. Climate Change in a Public Goods Game: Investment Decision in Mitigation versus Adaptation By Hasson, Reviva; Löfgren, Åsa; Visser, Martine
  19. Robust Control in Global Warming Management: An Analytical Dynamic Integrated Assessment By Hennlock, Magnus

  1. By: Philip J. Reny (Department of Economics, University of Chicago); Eyal Winter (Center for the Study of Rationality, Hebrew University); Myrna Wooders (Department of Economics, Vanderbilt University)
    Abstract: An outcome of a game is partnered if there are no asymmetric dependencies between any two players. For a cooperative game, a payoff is in the partnered core of the game if it is partnered, feasible and cannot be improved upon by any coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are no more than three partnerships, the sums of the payoffs to partnerships are constant across all core payoffs. When there are no more than three players, the partnered core satisfies additional properties.
    Keywords: Partnership, core, cooperative game, convex game, separating collections of sets, minimal partnership, coalition structure games, partitioning games, kernel
    JEL: C71
    Date: 2009–10
  2. By: Grandjean Gilles; Mauleon Ana; Vannetelbosch Vincent (METEOR)
    Abstract: Curb sets [Basu and Weibull, Econ. Letters 36 (1991), 141-146] are product sets of pure strategies containing all individual best-responses against beliefs restricted to the recommendations to the remaining players. The concept of minimal curb sets is a set-theoretic coarsening of the notion of strict Nash equilibrium. We introduce the concept of minimal strong curb sets which is a set-theoretic coarsening of the notion of strong Nash equilibrium. Strong curb sets are product sets of pure strategies such that each player.s set of recommended strategies must contain all coalitional best-responses of each coalition to whatever belief each coalition member may have that is consistent with the recommendations to the other players. Minimal strong curb sets are shown to exist and are compared with other well known solution concepts. We also provide a dynamic learning process leading the players to playing strategies from a minimal strong curb set.
    Keywords: mathematical economics;
    Date: 2009
  3. By: David R. Baqaee (University of Canterbury)
    Abstract: Consider an n-person Nash Bargaining problem where players bargain over the division of a cake whose size is stochastic. In such a game, the players are not only bargaining for more cake, but they are also sharing risk. This paper examines and provides the solution to this problem and highlights a few special cases.
    Keywords: Risk sharing; uncertainty; Nash bargaining
    JEL: C78 D81
    Date: 2009–12–02
  4. By: Dan Protopopescu
    Abstract: The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.
    Keywords: Dynamic Nash game, optimal path, closed-loop control, endogenous risk-and effort-aversion, adaptive risk-and effort management, optimal risk-and effort-sharing.
    JEL: C71 C73 D81 D82
    Date: 2009–12–11
  5. By: Tim Hellmann (Institute of Mathematical Economics, Bielefeld University)
    Abstract: This paper studies the properties of convexity (concavity) and strategic complements (substitutes) in network formation and the implications for the structure of pairwise stable networks. First, different definitions of convexity (concavity) in own links from the literature are put into the context of diminishing marginal utility of own links. Second, it is shown that there always exists a pairwise stable network as long as the utility function of each player satisfies convexity in own links and strategic complements. For network societies with a profile of utility functions satisfying concavity in own links and strategic complements, a local uniqueness property of pairwise stable networks is derived. The results do neither require any specification on the utility function nor any other additional assumptions such as homogeneity.
    Keywords: Networks, Network Formation, Game Theory, Supermodularity, Increasing Differences, Stability, Existence, Uniqueness
    JEL: D85 C72 L14
    Date: 2009–11
  6. By: Myrna Wooders (Department of Economics, Vanderbilt University)
    Abstract: The equivalence of markets and games concerns the relationship between two sorts of structures that appear fundamentally different -- markets and games. Shapley and Shubik (1969) demonstrates that: (1) games derived from markets with concave utility functions generate totally balanced games where the players in the game are the participants in the economy and (2) every totally balanced game generates a market with concave utility functions. A particular form of such a market is one where the commodities are the participants themselves, a labor market for example. ÊÊBut markets are very special structures, more so when it is required that utility functions be concave. Participants may also get utility from belonging to groups, such as marriages, or clubs, or productive coalitions. It may be that participants in an economy even derive utility (or disutility) from engaging in processes that lead to the eventual exchange of commodities. The question is when are such economic structures equivalent to markets with concave utility functions? This paper summarizes research showing that a broad class of large economies generate balanced market games. The economies include, for example, economies with clubs where individuals may have memberships in multiple clubs, with indivisible commodities, with nonconvexities and with non-monotonicities. The main assumption are: (1) that an option open to any group of players is to break into smaller groups and realize the sum of the worths of these groups, that is, essential superadditivity is satisfied and :(2) relatively small groups of participants can realize almost all gains to coalition formation. The equivalence of games with many players and markets with many participants indicates that relationships obtained for markets with concave utility functions and many participants will also hold for diverse social and economic situations with many players. These relationships include: (a) equivalence of the core and the set of competitive outcomes; (b) the Shapley value is contained in the core or approximate cores; (c) the equal treatment property holds -- that is, both market equilibrium and the core treat similar players similarly. These results can be applied to diverse economic models to obtain the equivalence of cooperative outcomes and competitive, price taking outcomes in economies with many participants and indicate that such results hold in yet more generality.
    Keywords: Markets, games, market games, clubs, core, market-game equivalence, Shapley value, price taking equilibrium, small group effectiveness, inessentiality of large groups, per capita boundedness, competitive equilibrium, games with side payments, balanced games, totally balanced games, local public goods, core convergence, equal treatment property, equal treatment core, approximate core, strong epsilon core, weak epsilon core, cooperative game, asymptotic negligibility
    JEL: C71 D2 D4 D51 D71
    Date: 2009–10
  7. By: Funk, Matt
    Abstract: This discourse offers a solution to The Problem of Sustainable Economic Development on islands. This hypothesis offers a foundational, sub-game solution to The Island Survival Game, a counterintuitive, dominant economic development strategy for ‘islands’ (and relatively insular states). This discourse also tables conceptual building blocks, prerequisite analytical tools, and a guiding principle for The Earth Island Survival Game, a bounded delay supergame which models The Problem of Sustainable Economic Development at the global level. We begin our exploration with an introduction to The Principle of Relative Insularity, a postulate which informs ESS for ‘island’ and ‘continental’ players alike. Next, we model ‘island’ economic development with two bio-geo-politico-economic models and respective strategies: The Mustique Co. Development Plan, and The Prince Edward Island Federal-Provincial Program for Social and Economic Advancement. These diametrically opposed strategies offer an extraordinary comparative study. One island serves as a highly descriptive model for The Problem of Sustainable Economic Development; the other model informs ESS. The Island Survival Game serves as a remarkable learning tool, offering lessons which promote Darwinian fitness, resource holding power, self-sufficiency, and cooperative behaviour, by illuminating the illusive path toward sustainable economic development.
    Keywords: Non-cooperative games; evolutionary game theory; relative insularity; islands; tragedy of the commons; sustainable economic development; resource holding power; evolutionarily stable strategy; long distance dispersal
    JEL: O1 O13 C72
    Date: 2009–07–04
  8. By: Dan Protopopescu
    Abstract: The objective of this paper is to clarify the interactive nature of the leader-follower relationship when both players are endogenously risk-averse. The analysis is placed in the context of a dynamic closed-loop Stackelberg game with private information. The case of a risk-neutral leader, very often discussed in the literature, is only a borderline possibility in the present study. Each player in the game is characterized by a risk-averse type which is unknown to his opponent. The goal of the leader is to implement an optimal incentive compatible risk-sharing contract. The proposed approach provides a qualitative analysis of adaptive risk behavior profiles for asymmetrically informed players in the context of dynamic strategic interactions modelled as incentive Stackelberg games.
    Keywords: Dynamic stochastic Stackelberg game, optimal path, closed-loop control, endogenous risk-aversion, adaptive risk management, optimal risk-sharing.
    JEL: C71 C73 D81 D82
    Date: 2009–12–11
  9. By: Carlos Pimienta (School of Economics, The University of New South Wales)
    Abstract: In a Bayesian assessment beliefs are computed from the strategy profile following Bayes’ rule at positive probability information sets and for every subgame. We characterize the set of extensive-forms (extensive-form games without a payoff assignment) for which the sets of Bayesian assessments and consistent assessments coincide. In doing so we disentangle the different restrictions imposed by consistency across information sets.
    Keywords: Backwards induction; Bayesian assessments; Consistent assessments; Sequential equilibrium; Extensive-forms
    JEL: C62 C72 D80
    Date: 2009–11
  10. By: Filippo Vergara Caffarelli (Bank of Italy JEL classification: C72, D83, D85)
    Abstract: This paper presents a model of non-cooperative network formation in which the marginal benefit of new links eventually decreases. Agents link with each other to gain information and update their links according to better-reply dynamics. In the long run the system settles to a unique network architecture that consists of a constellation of starred wheels. This is reminiscent of some real-world features. Collections of smaller disjoint networks connecting only a few agents are more common than global networks connecting all the agents in a community. Differences within a connected component such as the centre and the periphery are established.
    Keywords: networks, coordination, learning dynamics, non-cooperative games
    Date: 2009–11
  11. By: Martin Sefton (School of Economics, University of Nottingham); Ping Zhang (School of Economics, University of Nottingham)
    Abstract: We use laboratory experiments to compare allocation rules in uniform price divisible good auctions. “Standard” and “uniform” allocation rules admit different types of low-price equilibria, which are eliminated by a “hybrid” rule. We observe little evidence of revenue differences among the allocation rules. Under all three allocation rules, prices are competitive when bidders cannot explicitly communicate, and collusive when bidders can explicitly communicate. With explicit communication we find that collusive agreements are more fragile when the gain from a unilateral deviation is larger. We also find that the standard allocation rule is particularly vulnerable to collusive equilibria.
    Keywords: experiment, uniform price auction, multi-unit auction, divisible-good auction, allocation rule, communication
    JEL: D44 C72 C92
    Date: 2009–11
  12. By: Choi, Syngjoo; Lee, Jihong
    Abstract: We study experimentally how the network structure and length of pre-play communication affect behavior and outcome in a multi-player coordination game with conflicting preferences. Network structure matters but the interaction between network and time effects is more subtle. Under each time treatment, substantial variations are observed in both the rate of coordination and distribution of coordinated outcomes across networks. But increasing the communication length improves both efficiency an equity of coordination. In all treatments, coordination is mostly explained by convergence in communication. We also identify behaviors that explain variations in the distribution of coordinated outcomes both within and across networks.
    Keywords: experiment; pre-play communication; coordination; network; efficiency; equity
    JEL: C92 D83 C72
    Date: 2009–11–20
  13. By: Yuki Kumagai (University of Nottingham)
    Abstract: The purpose of this paper is to explore strategic incentives to use trade networks rather than markets and to shed light on the dynamic relations between two distinct trading systems: a formal system of markets and a decentralised system of networks. We investigate the issues by mainly focusing on the role of matching in a trade network. The existing literature emphasises the importance of information transmission in achieving efficiency in repeated personal transactions under perfect observability. By contrast, we show that a folk theorem may hold if we change the way traders are matched, without introducing any information sharing. We also examine different stages of an evolution of trading system. The study states conditions under which agents prefer to trade on networks rather than in markets.
    Keywords: Trade networks; Repeated games; Matching; Uncertainty; Transaction costs; Institutional dynamics
    JEL: F10 C73 D01
    Date: 2009–11
  14. By: De Martí, Joan; Zenou, Yves
    Abstract: We survey the literature on social networks by putting together the economics, sociological and physics/applied mathematics approaches, showing their similarities and differences. We expose, in particular, the two main ways of modeling network formation. While the physics/applied mathematics approach is capable of reproducing most observed networks, it does not explain why they emerge. On the contrary, the economics approach is very precise in explaining why networks emerge but does a poor job in matching real-world networks. We also analyze behaviors on networks, which take networks as given and focus on the impact of their structure on individuals’ outcomes. Using a game-theoretical framework, we then compare the results with those obtained in sociology.
    Keywords: centrality measures; game theory; network formation; random graph; weak and strong ties.
    JEL: A14 C72 D85 Z13
    Date: 2009–12
  15. By: Kris De Jaegher; Jurjen Kamphorst
    Abstract: The set of equilibrium networks in the two-way flow model of network formation (Bala and Goyal, 2000) is very sensitive to the introduction of decay. Even if decay is small enough so that equilibrium networks are minimal, the set of equilibrium architectures becomes much richer, especially when the benefit functions are nonlinear. However, not much is known about these architectures. In this paper we remedy this gap in the literature. We characterize the equilibrium architectures. Moreover, we show results on the relative stability of different types of architectures. Three of the results are that (i) at most one players receives multiple links, (ii) the absolute diameter of equilibrium networks can be arbitrarily large, and (iii) large (small) diameter networks are relatively stable under concave (convex) benefit functions.
    Keywords: Network formation, two-way flow model, decay, non-linear benefits
    JEL: C72 D85
    Date: 2009–11
  16. By: Laurent Lamy
    Abstract: When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.
    Date: 2009
  17. By: Edward Cartwright; Amrish Patel
    Abstract: Many charities report donations using categories. We question whether such category reporting increases donations in a signalling game where a donor is either generous or not generous. Conditions are derived under which category reporting will increase giving or decrease giving. Category reporting will increase giving if the probability a donor is generous is low and/or donor preferences depend a lot on type.
    Keywords: Public good; charity; category reporting; signalling.
    JEL: C72 H41
    Date: 2009–12
  18. By: Hasson, Reviva (Department of Economics, Faculty of Commerce, University of Cape Town); Löfgren, Åsa (Department of Economics, School of Business, Economics and Law, Göteborg University); Visser, Martine (Department of Economics, Faculty of Commerce, University of Cape Town)
    Abstract: We use behavioral and experimental economics to study a particular aspect of the economics of climate change: the potential tradeoff between countries’ investments in mitigation versus adaptation. While mitigation of greenhouse gases can be viewed as a public good, adaptation to climate change is a private good, benefiting only the country or the individual that invests in adaptation. We use a one-shot public-goods game that deviates from the standard public-goods game by introducing a stochastic term to account for probabilistic destruction in a climate-change setting. Probability density function is mapped to within-group levels of mitigation. We compare low-vulnerability and high-vulnerability treatments by varying the magnitude of disaster across treatments. Our results show that there is no significant difference in the level of mitigation across these treatments. Further, our results emphasize the important role of trust in enhancing cooperation.<p>
    Keywords: Public good; climate change; mitigation; adaptation; experiment; risk
    JEL: H41 Q54
    Date: 2009–12–08
  19. By: Hennlock, Magnus
    Abstract: Imperfect measurement of uncertainty (deeper uncertainty) in climate sensitivity is introduced in a two-sectoral integrated assessment model (IAM) with endogenous growth, based on an extension of DICE. The household expresses ambiguity aversion and can use robust control via a `shadow ambiguity premium' on social carbon cost to identify robust climate policy feedback rules that work well over a range such as the IPCC climate sensitivity range (IPCC, 2007a). Ambiguity aversion, in combination with linear damage, increases carbon cost in a similar way as a low pure rate of time preference. However, ambiguity aversion in combination with non-linear damage would also make policy more responsive to changes in climate data observations. Perfect ambiguity aversion results in an infinite expected shadow carbon cost and a zero carbon consumption path. Dynamic programming identifies an analytically tractable solution to the IAM.
    Keywords: climate policy, carbon cost, robust control, Knightian uncertainty, ambiguity aversion, integrated asssessment
    JEL: C73 C61 Q54
    Date: 2009–05–04

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