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Register a new userHysteresis effects of changing parameters of noncooperative games
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Added by
David Wolpert
Publication date
2010
fields
Informatics Engineering
and research's language is
English
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We adapt the method used by Jaynes to derive the equilibria of statistical physics to instead derive equilibria of bounded rational game theory. We analyze the dependence of these equilibria on the parameters of the underlying game, focusing on hysteresis effects. In particular, we show that by gradually imposing individual-specific tax rates on the players of the game, and then gradually removing those taxes, the players move from a poor equilibrium to one that is better for all of them.
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In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-movers move. What properties of a game determine whether it has such negative value of information for a particular player? Can a game have negative value of information for all players? To answer such questions, we generalize the definition of marginal utility of a good to define the marginal utility of a parameter vector specifying a game. So rather than analyze the global structure of the relationship between a games parameter vector and player behavior, as in previous work, we focus on the local structure of that relationship. This allows us to prove that generically, every game can have negative marginal value of information, unless one imposes a priori constraints on allowed changes to the games parameter vector. We demonstrate these and related results numerically, and discuss their implications.
We analyze in this paper finite horizon hierarchical signaling games between (information provider) senders and (decision maker) receivers in a dynamic environment. The underlying information evolves in time while sender and receiver interact repeatedly. Different from the classical communication (control) models, however, the sender (sensor) and the receiver (controller) have different objectives and there is a hierarchy between the players such that the sender leads the game by announcing his policies beforehand. He needs to anticipate the reaction of the receiver and the impact of the actions on the horizon while controlling the transparency of the disclosed information at each interaction. With quadratic cost functions and multivariate Gaussian processes, evolving according to first order auto-regressive models, we show that memoryless linear sender signaling rules are optimal (in the sense of game-theoretic hierarchical equilibrium) within the general class of measurable policies in the noncooperative communication context. In the noncooperative control context, we also analyze the hierarchical equilibrium for linear signaling rules and provide an algorithm to compute the optimal linear signaling rules numerically with global optimality guarantees.
Decentralized online learning for seeking generalized Nash equilibrium (GNE) of noncooperative games in dynamic environments is studied in this paper. Each player aims at selfishly minimizing its own time-varying cost function subject to time-varying coupled constraints and local feasible set constraints. Only local cost functions and local constraints are available to individual players, who can receive their neighbors information through a fixed and connected graph. In addition, players have no prior knowledge of cost functions and local constraint functions in the future time. In this setting, a novel distributed online learning algorithm for seeking GNE of the studied game is devised based on mirror descent and a primal-dual strategy. It is shown that the presented algorithm can achieve sublinearly bounded dynamic regrets and constraint violation by appropriately choosing decreasing stepsizes. Finally, the obtained theoretical result is corroborated by a numerical simulation.
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to nearby games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games.
Extensive-form games constitute the standard representation scheme for games with a temporal component. But do all extensive-form games correspond to protocols that we can implement in the real world? We often rule out games with imperfect recall, which prescribe that an agent forget something that she knew before. In this paper, we show that even some games with perfect recall can be problematic to implement. Specifically, we show that if the agents have a sense of time passing (say, access to a clock), then some extensive-form games can no longer be implemented; no matter how we attempt to time the game, some information will leak to the agents that they are not supposed to have. We say such a game is not exactly timeable. We provide easy-to-check necessary and sufficient conditions for a game to be exactly timeable. Most of the technical depth of the paper concerns how to approximately time games, which we show can always be done, though it may require large amounts of time. Specifically, we show that for some games the time required to approximately implement the game grows as a power tower of height proportional to the number of players and with a parameter that measures the precision of the approximation at the top of the power tower. In practice, that makes the games untimeable. Besides the conceptual contribution to game theory, we believe our methodology can have applications to preventing information leakage in security protocols.
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