Search results for "Mathematical Economics"
showing 10 items of 240 documents
Consensus in opinion dynamics as a repeated game
2018
Abstract We study an n -agent averaging process with dynamics subject to controls and adversarial disturbances. The model arises in multi-population opinion dynamics with macroscopic and microscopic intertwined dynamics. The averaging process describes the influence from neighbouring populations, whereas the input term indicates how the distribution of opinions in the population changes as a result of dynamical evolutions at a microscopic level (individuals’ changing opinions). The input term is obtained as the vector payoff of a two player repeated game. We study conditions under which the agents achieve robust consensus to some predefined target set. Such conditions build upon the approac…
On coincidence of feedback and global Stackelberg equilibria in a class of differential games
2021
This paper shows for a class of differential games that the global Stackelberg equilibrium (GSE) coincides with the feedback Stackelberg equilibrium (FSE), although the GSE assumes that the leader/regulator an- nounces at the initial time the regulatory instrument rule she will follow for the rest of the game, while in the FSE, the regulator at any time chooses the optimal level of the regulatory instrument rate. This coincidence is based on the fact that the FSE is calculated using dynamic programming what implies that although the regulator chooses the regulatory instrument rate level that maximizes social welfare, the first-order condition for the maximization of the right-hand side of t…
Collusion constrained equilibrium
2018
We study collusion within groups in non-cooperative games. The primitives are the preferences of the players, their assignment to non-overlapping groups and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This allows groups to put positive probability on alternatives that are suboptimal for the group in certain razor's edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained e…
Worst Case Analysis of Non-local Games
2013
Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a referee. The players cannot communicate but may share common random bits or a common quantum state. A referee sends an input x i to the i th player who then responds by sending an answer a i to the referee. The players win if the answers a i satisfy a condition that may depend on the inputs x i .
On the Coincidence of the Feedback Nash and Stackelberg Equilibria in Economic Applications of Differential Games
2002
In this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, conditions for obtaining the coincidence between the Stackelberg and Nash equilibria are defined in terms of the instantaneous pay-off function and the state equation of the game. Secondly, it is showed that for a class of differential games with state-interdependence both equilibria are identical independently of the player being the leader of the game. A survey of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting i…
Recursive and bargaining values
2021
Abstract We introduce two families of values for TU-games: the recursive and bargaining values. Bargaining values are obtained as the equilibrium payoffs of the symmetric non-cooperative bargaining game proposed by Hart and Mas-Colell (1996). We show that bargaining values have a recursive structure in their definition, and we call this property recursiveness. All efficient, linear, and symmetric values that satisfy recursiveness are called recursive values. We generalize the notions of potential, and balanced contributions property, to characterize the family of recursive values. Finally, we show that if a time discount factor is considered in the bargaining model, every bargaining value h…
TUG-OF-WAR, MARKET MANIPULATION, AND OPTION PRICING
2014
We develop an option pricing model based on a tug-of-war game involving the the issuer and holder of the option. This two-player zero-sum stochastic differential game is formulated in a multi-dimensional financial market and the agents try, respectively, to manipulate/control the drift and the volatility of the asset processes in order to minimize and maximize the expected discounted pay-off defined at the terminal date $T$. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a partial differential equation involving the non-linear and completely degenerate parabolic infinity Laplace operator.
The erosion of personal norms and cognitive dissonance
2016
ABSTRACTIn this article, we study how personal norms and behaviour interact and evolve when agents try to reduce cognitive dissonance, and how this dynamic relates to Nash equilibrium. We find that in long run, agents play, and norms prescribe, Nash equilibrium in material payoffs (in the absence of norms). Our model captures two main facts: (i) norms erode along the play of the game; (ii) the erosion of norms depends on the set of possible economic choices, so that the policy maker can potentially influence them.
Constrained consensus for bargaining in dynamic coalitional TU games
2011
We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. We assume that the players in the game interact only with their neighbors, where the neighbors may vary over time. The main contributions of the paper are the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining protocol to a random allocation that lies in the core of the robust game under some mild conditions on the players' communication graphs.
Values of games with probabilistic graphs
1999
Abstract In this paper we consider games with probabilistic graphs. The model we develop is an extension of the model of games with communication restrictions by Myerson (1977) . In the Myerson model each pair of players is joined by a link in the graph if and only if these two players can communicate directly. The current paper considers a more general setting in which each pair of players has some probability of direct communication. The value is defined and characterized in this context. It is a natural extension of the Myerson value and it turns out to be the Shapley value of a modified game.