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Aggregative Games and Best-Reply Potentials

by Martin Kaae Jensen
"... This paper introduces quasi-aggregative games and establishes conditions under which such games admit a best-reply potential. This implies existence of a pure strategy Nash equilibrium without any convexity or quasi-concavity assumptions. It also implies convergence of best-reply dynamics under so ..."
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This paper introduces quasi-aggregative games and establishes conditions under which such games admit a best-reply potential. This implies existence of a pure strategy Nash equilibrium without any convexity or quasi-concavity assumptions. It also implies convergence of best-reply dynamics under some additional assumptions. Most of the existing literature’s aggregation concepts are special cases of quasi-aggregative games, and many new situations are allowed for. An example is payoff functions that depend on own strategies as well as a linear combination of the mean and the variance of players’ strategies.

An efficient and almost budget balanced cost sharing method

by Hervé Moulin , 2007
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Fully Aggregative Games

by Richard Cornes, Roger Hartley, Richard Cornes, Roger Hartley, Richard Cornes, Roger Hartley - ANUCBE School of Economics Working Papers Series , 2009
"... We study aggregative games in which players ’ strategy sets are convex intervals of the real line and (not necessarily differentiable) payoffs depend only on a player’s own strategy and the sum of all players ’ strategies. We give sufficient conditions on each player’s pay-off function to ensure the ..."
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We study aggregative games in which players ’ strategy sets are convex intervals of the real line and (not necessarily differentiable) payoffs depend only on a player’s own strategy and the sum of all players ’ strategies. We give sufficient conditions on each player’s pay-off function to ensure the existence of a unique Nash equilibrium in pure strategies, emphasizing the geometric nature of these conditions. These conditions are almost best possible in the sense that the re-quirements on one player can be slightly weakened, but any further weakening may lead to multiple equilibria. The same conditions also permit the analysis of comparative statics and the competitive limit. We discuss the application of these conditions in a range of examples, chosen to illustrate various aspects their use. We also show that all restrictions on payoffs in aggregative games that guarantee the exis-tence of a unique equilibrium of which we are aware are covered by
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An agent-based model of payment systems

by Marco Galbiati, Kimmo Soramäki , 2007
"... We lay out and simulate a multi-agent, multi-period model of an RTGS payment system. At the beginning of the day, banks choose how much costly liquidity to allocate to the settlement process. Then, they use it to execute an exogenous, random stream of payment orders. If a bank’s liquidity stock is d ..."
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We lay out and simulate a multi-agent, multi-period model of an RTGS payment system. At the beginning of the day, banks choose how much costly liquidity to allocate to the settlement process. Then, they use it to execute an exogenous, random stream of payment orders. If a bank’s liquidity stock is depleted, payments are queued until new liquidity arrives from other banks, imposing costs on the delaying bank. We study the equilibrium level of liquidity posted in the system, performing some comparative statics and obtaining: i) a liquidity demand curve which links liquidity to delay costs; ii) insights on the efficiency of alternative system configurations; iii) insights on the effects of operational incidents on the amount of liquidity present in the system. † Bank of England.

Representing equilibrium aggregates in aggregate games with applications to common agency

by David Martimort, et al. - GAMES AND ECONOMIC BEHAVIOR , 2012
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Aggregate Representations of Aggregate Games

by David Martimort, Lars Stole - MPRA Paper , 2011
"... Abstract. An aggregate game is a normal-form game with the property that each player’s payoff is a function only of his own strategy and an aggregate function of the strategy profile of all players. Aggregate games possess a set of purely algebraic properties that can often provide simple characteri ..."
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Abstract. An aggregate game is a normal-form game with the property that each player’s payoff is a function only of his own strategy and an aggregate function of the strategy profile of all players. Aggregate games possess a set of purely algebraic properties that can often provide simple characterizations of equilibrium aggregates without first requiring that one solves for the equilibrium strategy profile. We demon-strate that the defining nature of payoffs in an aggregate game allows one to embed the strategic analysis into the aggregate-strategy space, converting an n-player game to a simpler object – a self-generating single-person maximization program. We apply these techniques to a number of economic settings including competition in supply functions or competitive agency games with nonlinear transfer functions. ∗This paper consolidates many of the results in the previous working papers “A note on aggregate-strategy games, ” 2005 and “Tricks with aggregate games, ” 2007.

Strategic supplements” in games with polylinear interactions”, Mimeo, Russian Academy of Sciences

by Nikolai S. Kukushkin , 2005
"... Strategic games are considered where: every player chooses from a compact subset of the real line; the partners ’ choices affect each player’s utility only through their scalar aggregate, which is affine in every single partner’s choice; if the choices of all players but two are fixed, then both fun ..."
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Strategic games are considered where: every player chooses from a compact subset of the real line; the partners ’ choices affect each player’s utility only through their scalar aggregate, which is affine in every single partner’s choice; if the choices of all players but two are fixed, then both functions expressing the dependence of one player’s aggregate on the other’s choice have the same slope; the best response correspondence of each player is nonempty-valued and increases in the aggregate. Every such game admits a “Cournot potential, ” i.e., Nash equilibria exist and all best response improvement paths, in a sense, lead to them. Journal of Economic Literature Classification Number: C 72.
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On the Existence of Monotone Selections

by Nikolai S. Kukushkin, Nikolai S. Kukushkin - Mimeo. 44 Laffont, J.-J. and J. Tirole , 2009
"... For a correspondence from a partially ordered set to a lattice, three sets of sufficient conditions for the existence of a monotone selection are obtained. (1) The correspondence is weakly ascending while every value satisfies a completeness condition, e.g., is chain-complete. (2) The correspondence ..."
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For a correspondence from a partially ordered set to a lattice, three sets of sufficient conditions for the existence of a monotone selection are obtained. (1) The correspondence is weakly ascending while every value satisfies a completeness condition, e.g., is chain-complete. (2) The correspondence is ascending while the target is a sublattice of the Cartesian product of a finite number of chains. (3) Both source and target are chains while the correspondence is generated by the maximization of a strongly acyclic interval order with the single crossing property. The theorems give new sufficient conditions for the existence of (epsilon) Nash equilibria. JEL Classification Number: C 72.

Shapley's "2 by 2 " theorem for game forms

by Nikolai S. Kukushkin
"... If a finite two person game form has the property that every 2-by-2 fragment is Nash consistent, then no derivative game admits an individual improvement cycle. ..."
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If a finite two person game form has the property that every 2-by-2 fragment is Nash consistent, then no derivative game admits an individual improvement cycle.

Increasing selections from increasing multifunctions

by Nikolai S. Kukushkin , 2012
"... We study when the existence of an increasing selection can be derived from the mono-tonicity of a multifunction w.r.t. an extension of the basic order from points to subsets. The most interesting results emerge when the target is a lattice and monotonicity is interpreted in one of the ways suggested ..."
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We study when the existence of an increasing selection can be derived from the mono-tonicity of a multifunction w.r.t. an extension of the basic order from points to subsets. The most interesting results emerge when the target is a lattice and monotonicity is interpreted in one of the ways suggested by A.F. Veinott, Jr. An increasing selection exists if (1) the multifunction is weakly ascending while every value satisfies a completeness condition, e.g., is chain-complete, or (2) the multifunction is ascending while the target is a sublattice of the Cartesian product of a finite number of chains. Key words: increasing selection; ascending multifunction; weakly ascending multifunction
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