Are game theoretic concepts suitable negotiation support tools? From Nash equilibrium refinements toward a cognitive concept of rationality

1993 ◽  
Vol 34 (3) ◽  
pp. 235-253 ◽  
Author(s):  
Bertrand R. Munier ◽  
Jean-Louis Rulli�re
Keyword(s):  
Nash Equilibrium ◽  
Negotiation Support ◽  
Equilibrium Refinements ◽  
Support Tools ◽  
Game Theoretic

scholarly journals Expressiveness and Nash Equilibrium in Iterated Boolean Games

2021 ◽  
Vol 22 (2) ◽  
pp. 1-38
Author(s):  
Julian Gutierrez ◽  
Paul Harrenstein ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Infinite Sequence ◽  
Multi Agent Systems ◽  
Temporal Logics ◽  
Agent Systems ◽  
Temporal Properties ◽  
Multi Agent ◽  
Game Theoretic ◽  
Boolean Games

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent  has a goal  , represented using (a fragment of) Linear Temporal Logic ( ) . The goal  captures agent  ’s preferences, in the sense that the models of  represent system behaviours that would satisfy  . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of  ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

Headings of UCAV Based on Nash Equilibrium

2018 ◽  
Vol 6 (3) ◽  
pp. 269-276
Author(s):  
Li Dai ◽  
Zheng Xie
Keyword(s):  
Nash Equilibrium ◽  
Linear Equations ◽  
Theoretic Model ◽  
Bounded Curvature ◽  
Smooth Path ◽  
Game Theoretic ◽  
Strategy Game ◽  
Simulation Results ◽  
Game Theoretic Model ◽  
Set Up

Abstract Given n vertices in a plane and UCAV going through each vertex once and only once and then coming back, the objective is to find the direction (heading) of motion in each vertex to minimize the smooth path of bounded curvature. This paper studies the headings of UCAV. First, the optimal headings for two vertices were given. On this basis, an n-player two-strategy game theoretic model was established. In addition, in order to obtain the mixed Nash equilibrium efficiently, n linear equations were set up. The simulation results demonstrated that the headings given in this paper are effective.

A time consistent derivative strategy

2020 ◽  
Vol 07 (01) ◽  
pp. 2050004
Author(s):  
Walter Mudzimbabwe
Keyword(s):  
Nash Equilibrium ◽  
Utility Function ◽  
Stochastic Volatility ◽  
Efficient Frontier ◽  
Equation System ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Game Theoretic ◽  
Time Inconsistent ◽  
Mean Variance

In this paper, we derive a time consistent investment strategy for an investor who can invest not only in a bond and stock but in a derivative as well. In order to capture typical features shown by stocks, the stock and by extension the derivative depends on stochastic volatility. We assume that the investor is interested in maximizing a mean–variance utility function. Since the problem is time-inconsistent, we formulate the problem in game theoretic way and seek a subgame Nash equilibrium as the strategy. By solving an extended HJB equation system, we derive explicit time-consistent strategy and the corresponding efficient frontier. In order to show efficiency of the derivative strategy, we compare it with a strategy for the case of a market without a derivative. Our results show that efficient frontier for an investor with a derivative is higher than without derivative.

scholarly journals Bounds and dynamics for empirical game theoretic analysis

2019 ◽  
Vol 34 (1) ◽  
Author(s):  
Karl Tuyls ◽  
Julien Perolat ◽  
Marc Lanctot ◽  
Edward Hughes ◽  
Richard Everett ◽  
...  
Keyword(s):  
Nash Equilibrium ◽  
Evolutionary Dynamics ◽  
Learning Algorithm ◽  
Agent Interactions ◽  
Approximate Nash Equilibrium ◽  
Blotto Game ◽  
Multi Agent ◽  
Payoff Structure ◽  
Game Theoretic ◽  
Colonel Blotto

AbstractThis paper provides several theoretical results for empirical game theory. Specifically, we introduce bounds for empirical game theoretical analysis of complex multi-agent interactions. In doing so we provide insights in the empirical meta game showing that a Nash equilibrium of the estimated meta-game is an approximate Nash equilibrium of the true underlying meta-game. We investigate and show how many data samples are required to obtain a close enough approximation of the underlying game. Additionally, we extend the evolutionary dynamics analysis of meta-games using heuristic payoff tables (HPTs) to asymmetric games. The state-of-the-art has only considered evolutionary dynamics of symmetric HPTs in which agents have access to the same strategy sets and the payoff structure is symmetric, implying that agents are interchangeable. Finally, we carry out an empirical illustration of the generalised method in several domains, illustrating the theory and evolutionary dynamics of several versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel Blotto game played by human players on Facebook (symmetric), the dynamics of several teams of players in the capture the flag game (symmetric), and an example of a meta-game in Leduc Poker (asymmetric), generated by the policy-space response oracle multi-agent learning algorithm.

scholarly journals A Game-Theoretical Approach to Multimedia Social Networks Security

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Enqiang Liu ◽  
Zengliang Liu ◽  
Fei Shao ◽  
Zhiyong Zhang
Keyword(s):  
Social Networks ◽  
Nash Equilibrium ◽  
Access Control ◽  
Control Model ◽  
Security Policies ◽  
Access Control Models ◽  
Multimedia Social Networks ◽  
Game Theoretical Approach ◽  
Game Theoretic ◽  
Stable Combination

The contents access and sharing in multimedia social networks (MSNs) mainly rely on access control models and mechanisms. Simple adoptions of security policies in the traditional access control model cannot effectively establish a trust relationship among parties. This paper proposed a novel two-party trust architecture (TPTA) to apply in a generic MSN scenario. According to the architecture, security policies are adopted through game-theoretic analyses and decisions. Based on formalized utilities of security policies and security rules, the choice of security policies in content access is described as a game between the content provider and the content requester. By the game method for the combination of security policies utility and its influences on each party’s benefits, the Nash equilibrium is achieved, that is, an optimal and stable combination of security policies, to establish and enhance trust among stakeholders.

BOUNDS ON THE CONVERGENCE TIME OF DISTRIBUTED SELFISH BIN PACKING

2011 ◽  
Vol 22 (03) ◽  
pp. 565-582 ◽  
Author(s):  
FLÁVIO K. MIYAZAWA ◽  
ANDRÉ L. VIGNATTI
Keyword(s):  
Nash Equilibrium ◽  
Bin Packing ◽  
Packing Problem ◽  
Convergence Time ◽  
Bin Packing Problem ◽  
Game Theoretic

We consider a game-theoretic bin packing problem with identical items, and we study the convergence time to a Nash equilibrium. In the model proposed, users choose their strategy simultaneously. We deal with two bins and multiple bins cases. We consider the case when users know the load of all bins and cases with less information. We consider two approaches, depending if the system can undo movements that lead to infeasible states. Let n and m be, respectively, the number of items and bins. In the two bins case, we show an O( log log n) and an O(n) bounds when undo movements are allowed and when they are not allowed, resp. In multiple bins case, we show an O( log n) and an O(nm) bounds when undo movements are allowed and when they are not allowed, resp. In the case with less information, we show an O(m log n) and an O(n3m) bounds when undo movements are allowed and when they are not allowed, resp. Also, in the case with less information where the information about completely filled/empty bins is not available, we show an O(m2 log n) and an O(n3m3) bounds when undo movements are allowed and when they are not allowed, resp.

scholarly journals New Directions for Modelling Strategic Behavior: Game-Theoretic Models of Communication, Coordination, and Cooperation in Economic Relationships

2016 ◽  
Vol 30 (4) ◽  
pp. 131-150 ◽  
Author(s):  
Vincent P. Crawford
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Strategic Behavior ◽  
Economic Problem ◽  
Noncooperative Game ◽  
Economic Relationships ◽  
Future Developments ◽  
New Directions ◽  
Game Theoretic

In this paper, I discuss the state of progress in applications of game theory in economics and try to identify possible future developments that are likely to yield further progress. To keep the topic manageable, I focus on a canonical economic problem that is inherently game-theoretic, that of fostering efficient coordination and cooperation in relationships, with particular attention to the role of communication. I begin with an overview of noncooperative game theory's principal model of behavior, Nash equilibrium. I next discuss the alternative “thinking” and “learning” rationales for how real-world actors might reach equilibrium decisions. I then review how Nash equilibrium has been used to model coordination, communication, and cooperation in relationships, and discuss possible developments

scholarly journals Smoothing Method for Approximate Extensive-Form Perfect Equilibrium

2017 ◽  
Author(s):  
Christian Kroer ◽  
Gabriele Farina ◽  
Tuomas Sandholm
Keyword(s):  
Nash Equilibrium ◽  
Imperfect Information ◽  
Large Scale ◽  
Nash Equilibria ◽  
Convex Polytope ◽  
Solution Concept ◽  
Extensive Form ◽  
Game Tree ◽  
Equilibrium Refinements ◽  
Perfect Equilibria

Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium. Equilibrium refinements can mend this issue, but have experienced little practical adoption. This is largely due to a lack of scalable algorithms.Sparse iterative methods, in particular first-order methods, are known to be among the most effective algorithms for computing Nash equilibria in large-scale two-player zero-sum extensive-form games. In this paper, we provide, to our knowledge, the first extension of these methods to equilibrium refinements. We develop a smoothing approach for behavioral perturbations of the convex polytope that encompasses the strategy spaces of players in an extensive-form game. This enables one to compute an approximate variant of extensive-form perfect equilibria. Experiments show that our smoothing approach leads to solutions with dramatically stronger strategies at information sets that are reached with low probability in approximate Nash equilibria, while retaining the overall convergence rate associated with fast algorithms for Nash equilibrium. This has benefits both in approximate equilibrium finding (such approximation is necessary in practice in large games) where some probabilities are low while possibly heading toward zero in the limit, and exact equilibrium computation where the low probabilities are actually zero.

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