4,579 research outputs found
An exact solution method for binary equilibrium problems with compensation and the power market uplift problem
We propose a novel method to find Nash equilibria in games with binary
decision variables by including compensation payments and
incentive-compatibility constraints from non-cooperative game theory directly
into an optimization framework in lieu of using first order conditions of a
linearization, or relaxation of integrality conditions. The reformulation
offers a new approach to obtain and interpret dual variables to binary
constraints using the benefit or loss from deviation rather than marginal
relaxations. The method endogenizes the trade-off between overall (societal)
efficiency and compensation payments necessary to align incentives of
individual players. We provide existence results and conditions under which
this problem can be solved as a mixed-binary linear program.
We apply the solution approach to a stylized nodal power-market equilibrium
problem with binary on-off decisions. This illustrative example shows that our
approach yields an exact solution to the binary Nash game with compensation. We
compare different implementations of actual market rules within our model, in
particular constraints ensuring non-negative profits (no-loss rule) and
restrictions on the compensation payments to non-dispatched generators. We
discuss the resulting equilibria in terms of overall welfare, efficiency, and
allocational equity
Solving Large Extensive-Form Games with Strategy Constraints
Extensive-form games are a common model for multiagent interactions with
imperfect information. In two-player zero-sum games, the typical solution
concept is a Nash equilibrium over the unconstrained strategy set for each
player. In many situations, however, we would like to constrain the set of
possible strategies. For example, constraints are a natural way to model
limited resources, risk mitigation, safety, consistency with past observations
of behavior, or other secondary objectives for an agent. In small games,
optimal strategies under linear constraints can be found by solving a linear
program; however, state-of-the-art algorithms for solving large games cannot
handle general constraints. In this work we introduce a generalized form of
Counterfactual Regret Minimization that provably finds optimal strategies under
any feasible set of convex constraints. We demonstrate the effectiveness of our
algorithm for finding strategies that mitigate risk in security games, and for
opponent modeling in poker games when given only partial observations of
private information.Comment: Appeared in AAAI 201
Quality-Of-Service Provisioning in Decentralized Networks: A Satisfaction Equilibrium Approach
This paper introduces a particular game formulation and its corresponding
notion of equilibrium, namely the satisfaction form (SF) and the satisfaction
equilibrium (SE). A game in SF models the case where players are uniquely
interested in the satisfaction of some individual performance constraints,
instead of individual performance optimization. Under this formulation, the
notion of equilibrium corresponds to the situation where all players can
simultaneously satisfy their individual constraints. The notion of SE, models
the problem of QoS provisioning in decentralized self-configuring networks.
Here, radio devices are satisfied if they are able to provide the requested
QoS. Within this framework, the concept of SE is formalized for both pure and
mixed strategies considering finite sets of players and actions. In both cases,
sufficient conditions for the existence and uniqueness of the SE are presented.
When multiple SE exist, we introduce the idea of effort or cost of satisfaction
and we propose a refinement of the SE, namely the efficient SE (ESE). At the
ESE, all players adopt the action which requires the lowest effort for
satisfaction. A learning method that allows radio devices to achieve a SE in
pure strategies in finite time and requiring only one-bit feedback is also
presented. Finally, a power control game in the interference channel is used to
highlight the advantages of modeling QoS problems following the notion of SE
rather than other equilibrium concepts, e.g., generalized Nash equilibrium.Comment: Article accepted for publication in IEEE Journal on Selected Topics
in Signal Processing, special issue in Game Theory in Signal Processing. 16
pages, 6 figure
Satisfaction Equilibrium: A General Framework for QoS Provisioning in Self-Configuring Networks
This paper is concerned with the concept of equilibrium and quality of
service (QoS) provisioning in self-configuring wireless networks with
non-cooperative radio devices (RD). In contrast with the Nash equilibrium (NE),
where RDs are interested in selfishly maximizing its QoS, we present a concept
of equilibrium, named satisfaction equilibrium (SE), where RDs are interested
only in guaranteing a minimum QoS. We provide the conditions for the existence
and the uniqueness of the SE. Later, in order to provide an equilibrium
selection framework for the SE, we introduce the concept of effort or cost of
satisfaction, for instance, in terms of transmit power levels, constellation
sizes, etc. Using the idea of effort, the set of efficient SE (ESE) is defined.
At the ESE, transmitters satisfy their minimum QoS incurring in the lowest
effort. We prove that contrary to the (generalized) NE, at least one ESE always
exists whenever the network is able to simultaneously support the individual
QoS requests. Finally, we provide a fully decentralized algorithm to allow
self-configuring networks to converge to one of the SE relying only on local
information.Comment: Accepted for publication in Globecom 201
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