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on Game Theory |
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Issue of 2012‒12‒15
thirteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Huseynov, T.; Talman, A.J.J. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: A new solution is presented for transferable utility games with graph communication where the cooperation possibilities are represented by a graph. Players are only able to cooperate and obtain some worth in a coalition if they form a connected set in the given graph. To determine the payoff for each player, a single-valued solution, the communication tree value, is proposed for this class of games. The idea is that to form the grand coalition of all players a player can join a set of players only if this player is connected in the graph to at least one of the players in the set. To a set of players, starting with an arbitrary single player, from each maximally connected subset of remaining players one player joins who is connected to one or more of the players in that set. In this way a (rooted) tree on the set of players is obtained, called a communication tree. For a given game each communication tree of the graph induces a marginal contribution vector, in which any player receives a payoff equal to what he contributes in worth when he joins his subordinates in the tree. The average payoff over all communication trees of the graph determines the value. In case the underlying graph is cycle-complete the value coincides with the average tree solution. When there is complete communication between all players, which is the special case of cycle-completeness, players join one by one, yielding the Shapley value. A weak form of convexity is introduced, under which the value is guaranteed to be an element of the core. For games with complete graph communication the condition coincides with convexity and in case the underlying graph is cycle-free it is weaker than super-additivity. |
| Keywords: | Cooperative game;communication structure;Myerson value;core stability;convexity;rooted tree. |
| JEL: | C71 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012095&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Chris Dietz (VU University Amsterdam) |
| Abstract: | It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of (weighted) digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with a permission structure into a model called games with a local permission structure, where every player needs permission from its predecessors only in order to generate worth, but does not need its predecessors in order to give permission to its own successors. We introduce and axiomatize a Shapley value type solution for these games, generalizing the conjunctive permission value for games with a permission structure and the beta-measure for weighted digraphs. |
| Keywords: | Cooperative TU-game; peer group game; digraph game; game with a permission structure; local permission structure |
| JEL: | C71 |
| Date: | 2012–11–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120126&r=gth |
| By: | Iñarra García, María Elena; Larrea Jaurrieta, María Concepción; Saracho de la Torre, Ana Isabel |
| Abstract: | We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2 2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have infinite sets. |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:9148&r=gth |
| By: | Kleppe, J.; Borm, P.E.M.; Hendrickx, R.L.P. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: Proper equilbrium plays an importent role in the literature on non-cooperative games. The underlying thought experiment is, however, unsatisfying, as it gives no justification for its fundamental idea that severe mistakes are made with a significantly smaller probability than innocuous ones. In this paper we provide a justification for this idea based on strategic choices of the players. In this way we provide a strategic foundation for proper equilibrium. |
| Keywords: | proper equilibrium;fall back proper equilibrium. |
| JEL: | C72 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012093&r=gth |
| By: | Francesca Busetto; Giulio Codognato; Sayantan Ghosal |
| Abstract: | In this paper, in an exchange economy with atoms and an atomless part, we analyze the relationship between the set of the Cournot-Nash equilibrium allocations of a strategic market game and the set of the Walras equilibrium allocations of the exchange economy with which it is associated. In an example, we show that, even when atoms are countably infinite, Cournot-Nash equilibria yield different allocations from the Walras equilibrium allocations of the underlying exchange economy. We partially replicate the exchange economy by increasing the number of atoms without affecting the atomless part while ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market game associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy. |
| Keywords: | Cournot-Nash equilibrium, strategic market games, limit theorem |
| JEL: | C72 D51 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2012-49&r=gth |
| By: | Ciarreta Antuñano, Aitor; García Enríquez, Javier; Gutiérrez Hita, Carlos |
| Abstract: | In a two-stage delegation game model with Nash bargaining between a manager and an owner, an equivalence result is found between this game and Fershtman and Judd's strategic delegation game (Fershtman and Judd, 1987). Interestingly, although both games are equivalent in terms of profits under certain conditions, managers obtain greater rewards in the bargaining game. This results in a redistribution of profits between owners and managers. |
| Keywords: | strategic delegation, bargaining, product substitutability, price |
| JEL: | C72 L13 M54 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:dfaeii:9151&r=gth |
| By: | Platz, Trine Tornøe (Department of Business and Economics); Hamers, Herbert (Department of Econometrics & OR and CentER); Quant, Marieke (Department of Econometrics & OR and CentER) |
| Abstract: | The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets. |
| Keywords: | Core; core cover; larginal vectors |
| JEL: | C71 |
| Date: | 2012–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2012_025&r=gth |
| By: | Dai, Darong |
| Abstract: | In the current paper, we study the asymmetric normal-form game between two heterogeneous groups of populations by employing the stochastic replicator dynamics driven by Lévy process. A new game equilibrium, i.e., the game equilibrium of a stochastic differential cooperative game on time, is derived by introducing optimal-stopping technique into evolutionary game theory, which combines with the Pareto optimal standard leads us to the existence of Pareto optimal endogenous matching. |
| Keywords: | Stochastic differential cooperative game on time; Endogenous matching; Fair matching; Pareto optimality; Adaptive learning |
| JEL: | C78 C70 C62 |
| Date: | 2012–12–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:43125&r=gth |
| By: | Platz, Trine Tornøe (Department of Business and Economics); Hamers, Herbert (Department of Econometrics & OR and CentER) |
| Abstract: | This paper introduces cooperative games arising from multi-depot Chinese postman problems and explores the properties of these games. A multi-depot Chinese postman problem (MDCP) is represented by a connected (di)graph G, a set of k depots that is a subset of the vertices of G, and a non-negative weight function on the edges of G. A solution to the MDCP is a minimum weight tour of the (di)graph that visits all edges (arcs) of the graph and that consists of a collection of subtours such that the subtours originate from different depots, and each subtour starts and ends at the same depot. A cooperative Chinese postman (CP) game is induced by a MDCP by associating every edge of the graph with a different player. This paper characterizes globally and locally k-CP balanced and submodular (di)graphs. A (di)graph G is called globally (locally) k-CP balanced (respectively submodular), if the induced CP game of the corresponding MDCP problem on G is balanced (respectively submodular) for any (some) choice of the locations of the k depots and every non-negative weight function. |
| Keywords: | Chinese postman problem; cooperative game; submodularity; balancedness |
| JEL: | C71 |
| Date: | 2012–12–02 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2012_024&r=gth |
| By: | Gabriele Camera (Economic Science Institute, Chapman University and University of Basel); Marco Casari (University of Bologna); Maria Bigoni (University of Bologna) |
| Abstract: | In an experiment, a group of strangers was randomly divided in pairs to play a prisoners’ dilemma; this process was indefinitely repeated. Cooperation did not increase when subjects could send public messages amounting to binding promises of future play. |
| Keywords: | coordination, cheap-talk, deception, repeated game, social norms |
| JEL: | C90 C70 D80 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:12-27&r=gth |
| By: | Boonen, T.J.; De Waegenaere, A.M.B.; Norde, H.W. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: This paper analyzes risk capital allocation problems. For risk capital allocation problems, the aim is to allocate the risk capital of a firm to its divisions. Risk capital allocation is of central importance in risk-based performance measurement. We consider a case in which the aggregate risk capital is determined via a coherent risk measure. The academic literature advocates an allocation rule that, in game-theoretic terms, is equivalent to using the Aumann-Shapley value as solution concept. This value is however not well-defined in case a differentiability condition is not satisfied. As an alternative, we introduce an allocation rule inspired by the Shapley value in a fuzzy setting. We take a grid on a fuzzy participation set, define paths on this grid and construct an allocation rule based on a path. Then, we define a rule as the limit of the average over these allocations, when the grid size converges to zero. We introduce this rule for a broad class of coherent risk measures. We show that if the Aumann-Shapley value is well-defined, the allocation rule coincides with it. If the Aumann-Shapley value is not defined, which is due to non-differentiability problems, the allocation rule specifies an explicit allocation. It corresponds with the Mertens value, which is originally characterized in an axiomatic way (Mertens, 1988), whereas we provide an asymptotic argument. |
| Keywords: | capital allocation;risk capital;Aumann-Shapley value;non-differentiability;fuzzy games. |
| JEL: | C71 G32 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012091&r=gth |
| By: | Marcel Nutz; Jianfeng Zhang |
| Abstract: | We study the existence of optimal actions in a zero-sum game $\inf_\tau \sup_P E^P[X_\tau]$ between a stopper and a controller choosing a probability measure. In particular, we consider the optimal stopping problem $\inf_\tau \mathcal{E}(X_\tau)$ for a class of sublinear expectations $\mathcal{E}(\cdot)$ including the $G$-expectation. We show that the game has a value. Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope $Y$ and prove that the first hitting time $\inf{t:\, Y_t=X_t}$ is an optimal stopping time. The existence of a saddle point is shown under a compactness condition. Finally, the results are applied to the subhedging of American options under volatility uncertainty. |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1212.2140&r=gth |
| By: | Funaki, Y.; Houba, H.E.D.; Motchenkova, E. (Tilburg University, Tilburg Law and Economics Center) |
| Abstract: | Abstract: We consider price-fee competition in bilateral oligopolies with perfectly-divisible goods, non-expandable infrastructures, concentrated agents on both sides, and constant marginal costs. We define and characterize stable market outcomes. Buyers exclusively trade with the supplier with whom they achieve maximal bilateral joint welfare. Prices equal marginal costs. Threats to switch suppliers set maximal fees. These also arise from a negotiation model that extends price competition. Competition in both prices and fees necessarily emerges. It improves welfare compared to price competition, but consumer surpluses do not increase. The minimal infrastructure achieving maximal aggregate welfare differs from the one that protects buyers most. |
| Keywords: | Assignment Games;Infrastructure;Negotiations;Non-linear pricing;Market Power. |
| JEL: | C78 L10 L14 D43 R10 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubtil:2012041&r=gth |