Game-Theoretic Control of the Object’s Random Jump Structure in the Class of Pure Strategies

2020 ◽  
Vol 59 (4) ◽  
pp. 494-503
Author(s):  
V. A. Boldinov ◽  
V. A. Bukhalev ◽  
A. A. Skrynnikov
Keyword(s):  
Game Theoretic ◽  
Pure Strategies ◽  
Random Jump

scholarly journals A guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium

2020 ◽  
Vol 12 (1) ◽  
pp. 60-90
Author(s):  
Сергей Николевич Смирнов ◽  
Sergey Smirnov
Keyword(s):  
Transaction Costs ◽  
A Priori ◽  
Contingent Claim ◽  
Mixed Strategies ◽  
Deterministic Approach ◽  
Game Equilibrium ◽  
Game Theoretic ◽  
Price History ◽  
Pure Strategies ◽  
Trading Constraints

For a discrete-time superreplication problem, a guaranteed deterministic formulation is considered: the problem is to ensure a cheapest coverage of the contingent claim on an option under all scenarios which are set using a priori defined compacts, depending on the price history: price increments at each moment of time must lie in the corresponding compacts. The market is considered with trading constraints and without transaction costs. The statement of the problem is game-theoretic in nature and leads directly to the Bellman - Isaacs equations. In this article, we introduce a mixed extension of the ``market'' pure strategies. Several results concerning game equilibrium are obtained.

scholarly journals The Price of Usability: Designing Operationalizable Strategies for Security Games

2018 ◽  
Author(s):  
Sara Marie Mc Carthy ◽  
Corine M. Laan ◽  
Kai Wang ◽  
Phebe Vayanos ◽  
Arunesh Sinha ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Mixed Strategy ◽  
Static Solution ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Security Personnel ◽  
Security Games ◽  
Game Theoretic ◽  
Pure Strategies ◽  
Security Game

We consider the problem of allocating scarce security resources among heterogeneous targets to thwart a possible attack. It is well known that deterministic solutions to this problem being highly predictable are severely suboptimal. To mitigate this predictability, the game-theoretic security game model was proposed which randomizes over pure (deterministic) strategies, causing confusion in the adversary. Unfortunately, such mixed strategies typically involve randomizing over a large number of strategies, requiring security personnel to be familiar with numerous protocols, making them hard to operationalize. Motivated by these practical considerations, we propose an easy to use approach for computing  strategies that are easy to operationalize and that bridge the gap between the static solution and the optimal mixed strategy. These strategies only randomize over an optimally chosen subset of pure strategies whose cardinality is selected by the defender, enabling them to conveniently tune the trade-off between ease of operationalization and efficiency using a single design parameter. We show that the problem of computing such operationalizable strategies is NP-hard, formulate it as a mixed-integer optimization problem, provide an algorithm for computing epsilon-optimal equilibria, and an efficient heuristic. We evaluate the performance of our approach on the problem of screening for threats at airport checkpoints and show that the Price of Usability, i.e., the loss in optimality to obtain a strategy that is easier to operationalize, is typically not high.

scholarly journals A GAME-THEORETIC APPROACH TO THE CHOICE OF UNION-OLIGOPOLY BARGAINING AGENDA

2018 ◽  
Vol 77 (305) ◽  
pp. 97
Author(s):  
Domenico Buccella ◽  
Luciano Fanti
Keyword(s):  
Mixed Duopoly ◽  
Limited Area ◽  
Theoretic Approach ◽  
Asymmetric Equilibria ◽  
Game Theoretic ◽  
Stage Game ◽  
Pure Strategies ◽  
Efficient Bargaining ◽  
Game Theoretic Approach ◽  
Selection Of

<p align="center"><strong>ABSTRACT</strong><strong></strong></p><p>This paper investigates the selection of the bargaining agenda in a unionized industry with decentralized negotiations for different competition modes. The firms choose the agenda (right-to-manage, RTM, <em>versus</em> efficient bargaining, EB), considering alternative timing of the bargaining game in the case of mixed duopoly. In fact, the EB (RTM) firm can be either Stackelberg wage follower (leader) or Stackelberg output leader (follower). A two-stage game is developed in which the typology as well as the timing of the negotiations is endogenous. It is shown that, in pure strategies, no equilibria arise for a wide set of the parameters’ space while RTM appears as the unique equilibrium agenda for a different combination of the parameters; moreover, multiple, asymmetric equilibria emerge in a limited area of the parameters’ space. These results are in sharp contrast to the received literature in which EB can arise as an industry bargaining institution in equilibrium.</p><p align="center"> </p><p align="center">UN ENFOQUE DE TEORÍA DE JUEGOS PARA LA SELECCIÓN DE LA AGENDA DE NEGOCIACIÓN DEL OLIGOPOLIO SINDICAL</p><p align="center"><strong> </strong><strong>RESUMEN</strong></p>Este artículo investiga la selección de la agenda de negociación en una industria sindicalizada con negociaciones descentralizadas para diferentes modos de competencia. Las empresas eligen la agenda (negociación con derecho de administrar, NDA, frente a negociación eficiente, NE) considerando casos alternativos de la sucesión de eventos en el juego de negociación con duopolio mixto. De hecho, la empresa NE (NDA) puede ser seguidora de salarios Stackelberg (líder) o líder de cantidades Stackelberg (seguidora). Se desarrolla un juego de dos etapas en el que la tipología y el momento de las negociaciones son endógenos. Se muestra que en estrategias puras no surgen equilibrios para un amplio conjunto del espacio de los parámetros, mientras que NDA aparece como la agenda de equilibrio única para una combinación diferente de los parámetros; además, los equilibrios múltiples y asimétricos emergen en un área limitada del espacio de los parámetros. Estos resultados contrastan con la literatura existente, en la que NE puede surgir como una institución de negociación de la industria en equilibrio.

Generalized Replicator Dynamics as a Model of Specialization and Diversity in Societies

1998 ◽  
Vol 01 (04) ◽  
pp. 325-359 ◽  
Author(s):  
Vivek S. Borkar ◽  
Sanjay Jain ◽  
Govindan Rangarajan
Keyword(s):  
Mixed Strategy ◽  
Replicator Dynamics ◽  
Pure Strategy ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Theoretic Model ◽  
Final States ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
Pure Strategies

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community of N agents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors if N is sufficiently large, and be regarded as innovations that enhance the diversity of the community.

scholarly journals Phenotypic heterogeneity implements a game theoretic mixed strategy in a clonal microbial population

2014 ◽  
Author(s):  
David Healey ◽  
Jeff Gore
Keyword(s):  
Experimental Evidence ◽  
Evolutionary Game ◽  
Phenotypic Heterogeneity ◽  
Microbial Populations ◽  
Bet Hedging ◽  
Hedging Strategy ◽  
Unpredictable Environments ◽  
Game Theoretic ◽  
Pure Strategies ◽  
Genetic Mutants

Genetically identical cells in microbial populations often exhibit a remarkable degree of phenotypic heterogeneity even in homogenous environments. While such heterogeneity is often thought to be a bet-hedging strategy against unpredictable environments, evolutionary game theory also predicts phenotypic heterogeneity as a stable response to evolutionary "hawk-dove" games, in which rare strategies are favored over common ones. Here we provide experimental evidence for this game theoretic explanation in the context of the well-studied yeast GAL network. In an environment containing the two sugars glucose and galactose, the yeast GAL network displays stochastic bimodal activation. We show that genetic mutants playing the "pure" strategies of GAL-ON or GAL-OFF can each invade the opposite strategy when rare, indicating a hawk-dove game between the two. Consistent with the Nash equilibrium of an evolutionary game, the stable mix of pure strategists does not necessarily maximize the growth of the overall population. We also find that the wild type GAL network can invade populations of both pure strategists while remaining uninvasible by either. Taken together, our results provide experimental evidence that evolutionary hawk-dove games between identical cells can explain the phenotypic heterogeneity found in clonal microbial populations.

A Dynamic Equilibrium Pricing Model: A Game Theoretic Approach to Modelling Conventions' Room Rates

1996 ◽  
Vol 2 (3) ◽  
pp. 251-263 ◽  
Author(s):  
Zvi Schwartz
Keyword(s):  
Dynamic Equilibrium ◽  
Relative Size ◽  
Theoretic Approach ◽  
Credible Commitment ◽  
Equilibrium Pricing ◽  
Strategic Behaviour ◽  
Price Optimization ◽  
Game Theoretic ◽  
Pure Strategies ◽  
Game Theoretic Approach

Utilizing the theoretical framework of game theory, this study provides an economic model to describe the process of determining a convention's room rates. It provides a method to infer simultaneously the room rate and the number of rooms allocated at each price level. This approach exploits information both on consumers' utilities and expectations, and on the hotel's perceptions of its markets. Equilibria in pure strategies are derived for various combinations of the market segments' relative size, supply demand ratios, and levels of willingness to pay. The study extends the existing literature on price optimization in hotels by including the customers as active participants in this strategic behaviour framework. The model demonstrates that the effectiveness of price optimization depends on the validity of the assumptions one makes about the segments' characteristics. The model identifies the market conditions under which yield management (allocation of rooms to room rates) maximizes the hotel's revenue. It shows the importance of a credible commitment by the hotel to maintain high room rates as time draws closer to the date of stay and shows how discounts can be used effectively to segment the market.

GAME THEORETIC BEST-RESPONSE DYNAMICS FOR EVACUEES' EXIT SELECTION

2010 ◽  
Vol 13 (01) ◽  
pp. 113-134 ◽  
Author(s):  
HARRI EHTAMO ◽  
SIMO HELIÖVAARA ◽  
TIMO KORHONEN ◽  
SIMO HOSTIKKA
Keyword(s):  
Mathematical Formulation ◽  
Response Functions ◽  
Response Dynamics ◽  
Emergency Evacuations ◽  
Best Response Dynamics ◽  
Best Response ◽  
Theoretic Concept ◽  
Game Theoretic ◽  
Pure Strategies ◽  
Number Of Iterations

We present a model for evacuees' exit selection in emergency evacuations. The model is based on the game theoretic concept of best-response dynamics, where each player updates his strategy periodically by reacting optimally to other players' strategies. A fixed point of the system of all players' best-response functions defines a Nash equilibrium (NE) of the game. In the model, the players are the evacuees and the strategies are the possible target exits. We present a mathematical formulation for the model and show that the game has a NE with pure strategies. We also analyze different iterative methods for finding the NE and derive an upper bound for the number of iterations needed to find the equilibrium. Numerical simulations are used to analyze the properties of the model.

Stability in the informal value transfer systems: norms of trust or institutions of control?

2017 ◽  
pp. 120-130
Author(s):  
A. Lyasko
Keyword(s):  
Social Control ◽  
Institutional Economics ◽  
Theoretic Model ◽  
Transfer System ◽  
Value Transfer ◽  
Partner Interaction ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
Informal Value Transfer System

Informal financial operations exist in the shadow of official regulation and cannot be protected by the formal legal instruments, therefore raising concerns about the enforcement of obligations taken by their participants. This paper analyzes two alternative types of auxiliary institutions, which can coordinate expectations of the members of informal value transfer systems, namely attitudes of trust and norms of social control. It offers some preliminary approaches to creating a game-theoretic model of partner interaction in the informal value transfer system. It also sheds light on the perspectives of further studies in this area of institutional economics.

Influential individuals: Approach to modeling

2018 ◽  
pp. 114-131
Author(s):  
O. Yu. Bondarenko
Keyword(s):  
Social Interactions ◽  
Social Status ◽  
Experimental Approach ◽  
Expert Knowledge ◽  
Formal Models ◽  
Leader Influence ◽  
Learning Game ◽  
Game Theoretic ◽  
Asymmetric Interactions ◽  
Influential Individuals

his article explores theoretical and experimental approach to modeling social interactions. Communication and exchange of information with other people affect individual’s behavior in numerous areas. Generally, such influence is exerted by leaders, outstanding individuals who have a higher social status or expert knowledge. Social interactions are analyzed in the models of social learning, game theoretic models, conformity models, etc. However, there is a lack of formal models of asymmetric interactions. Such models could help elicit certain qualities characterizing higher social status and perception of status by other individuals, find the presence of leader influence and analyze its mechanism.

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