Abstract: In this paper, a non-cooperative game method is
formulated where all players compete to transmit at higher
power. Every base station represents a player in the game.
The game is solved by obtaining the Nash equilibrium (NE)
where the game converges to optimality. The proposed method,
named Power Efficient Handover Game Theoretic (PEHO-GT)
approach, aims to control the handover in dense small cell
networks. Players optimize their payoff by adjusting the
transmission power to improve the performance in terms of
throughput, handover, power consumption and load balancing.
To select the desired transmission power for a player, the payoff
function considers the gain of increasing the transmission power.
Then, the cell selection takes place by deploying Technique for
Order Preference by Similarity to an Ideal Solution (TOPSIS).
A game theoretical method is implemented for heterogeneous
networks to validate the improvement obtained. Results reveal
that the proposed method gives a throughput improvement while
reducing the power consumption and minimizing the frequent
handover.
Abstract: We present a discrete game theoretical model with
homogeneous individuals who make simultaneous decisions. In
this model the strategy space of all individuals is a discrete
and dichotomous set which consists of two strategies. We fully
characterize the coherent, split and mixed strategies that form Nash
equilibria and we determine the corresponding Nash domains for all
individuals. We find all strategic thresholds in which individuals can
change their mind if small perturbations in the parameters of the
model occurs.
Abstract: An envy behavioral game theoretical model with two
types of homogeneous players is considered in this paper. The
strategy space of each type of players is a discrete set with only
two alternatives. The preferences of each type of players is given
by a discrete utility function. All envy strategies that form Nash
equilibria and the corresponding envy Nash domains for each type
of players have been characterized. We use geometry to construct
two dimensional envy tilings where the horizontal axis reflects the
preference for players of type one, while the vertical axis reflects
the preference for the players of type two. The influence of the envy
behavior parameters on the Cartesian position of the equilibria has
been studied, and in each envy tiling we determine the envy Nash
equilibria. We observe that there are 1024 combinatorial classes of
envy tilings generated from envy chromosomes: 256 of them are
being structurally stable while 768 are with bifurcation. Finally, some
conditions for the disparate envy Nash equilibria are stated.
Abstract: In decision making under strict uncertainty, decision makers have to choose a decision without any information about the states of nature. The classic criteria of Laplace, Wald, Savage, Hurwicz and Starr are introduced and compared in a case study of sewer network planning. Furthermore, results from different criteria are discussed and analyzed. Moreover, this paper discusses the idea that decision making under strict uncertainty (DMUSU) can be viewed as a two-player game and thus be solved by a solution concept in game theory: Nash equilibrium.
Abstract: The tradition competitive newsvendor game assumes decision makers are rational. However, there are behavioral biases when people make decisions, such as loss aversion, mental accounting and overconfidence. Overestimation of a subject’s own performance is one type of overconfidence. The objective of this research is to analyze the impact of the overestimated demand in the newsvendor competitive game with two players. This study builds a competitive newsvendor game model where newsvendors have private information of their demands, which is overestimated. At the same time, demands of each newsvendor forecasted by a third party institution are available. This research shows that the overestimation leads to demand steal effect, which reduces the competitor’s order quantity. However, the overall supply of the product increases due to overestimation. This study illustrates the boundary condition for the overestimated newsvendor to have the equilibrium order drop due to the demand steal effect from the other newsvendor. A newsvendor who has higher critical fractile will see its equilibrium order decrease with the drop of estimation level from the other newsvendor.
Abstract: The customers use the best compromise criterion
between price and quality of service (QoS) to select or change
their Service Provider (SP). The SPs share the same market and
are competing to attract more customers to gain more profit. Due
to the divergence of SPs interests, we believe that this situation is a
non-cooperative game of price and QoS. The game converges to an
equilibrium position known Nash Equilibrium (NE). In this work, we
formulate a game theoretic framework for the dynamical behaviors
of SPs. We use Genetic Algorithms (GAs) to find the price and
QoS strategies that maximize the profit for each SP and illustrate
the corresponding strategy in NE. In order to quantify how this NE
point is performant, we perform a detailed analysis of the price of
anarchy induced by the NE solution. Finally, we provide an extensive
numerical study to point out the importance of considering price and
QoS as a joint decision parameter.
Abstract: Game theory is the study of how people interact and
make decisions to handle competitive situations. It has mainly been
developed to study decision making in complex situations. Humans
routinely alter their behaviour in response to changes in their social
and physical environment. As a consequence, the outcomes of
decisions that depend on the behaviour of multiple decision makers
are difficult to predict and require highly adaptive decision-making
strategies. In addition to the decision makers may have preferences
regarding consequences to other individuals and choose their actions
to improve or reduce the well-being of others. Nash equilibrium is a
fundamental concept in the theory of games and the most widely used
method of predicting the outcome of a strategic interaction in the
social sciences. A Nash Equilibrium exists when there is no unilateral
profitable deviation from any of the players involved. On the other
hand, no player in the game would take a different action as long as
every other player remains the same.
Abstract: A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.
Abstract: The next generation wireless systems, especially the
cognitive radio networks aim at utilizing network resources more
efficiently. They share a wide range of available spectrum in an
opportunistic manner. In this paper, we propose a quality
management model for short-term sub-lease of unutilized spectrum
bands to different service providers. We built our model on
competitive secondary market architecture. To establish the
necessary conditions for convergent behavior, we utilize techniques
from game theory. Our proposed model is based on potential game
approach that is suitable for systems with dynamic decision making.
The Nash equilibrium point tells the spectrum holders the ideal price
values where profit is maximized at the highest level of customer
satisfaction. Our numerical results show that the price decisions of
the network providers depend on the price and QoS of their own
bands as well as the prices and QoS levels of their opponents- bands.
Abstract: An iterative algorithm is proposed and tested in Cournot Game models, which is based on the convergence of sequential best responses and the utilization of a genetic algorithm for determining each player-s best response to a given strategy profile of its opponents. An extra outer loop is used, to address the problem of finite accuracy, which is inherent in genetic algorithms, since the set of feasible values in such an algorithm is finite. The algorithm is tested in five Cournot models, three of which have convergent best replies sequence, one with divergent sequential best replies and one with “local NE traps"[14], where classical local search algorithms fail to identify the Nash Equilibrium. After a series of simulations, we conclude that the algorithm proposed converges to the Nash Equilibrium, with any level of accuracy needed, in all but the case where the sequential best replies process diverges.
Abstract: A road pricing game is a game where various stakeholders and/or regions with different (and usually conflicting) objectives compete for toll setting in a given transportation network to satisfy their individual objectives. We investigate some classical game theoretical solution concepts for the road pricing game. We establish results for the road pricing game so that stakeholders and/or regions playing such a game will beforehand know what is obtainable. This will save time and argument, and above all, get rid of the feelings of unfairness among the competing actors and road users. Among the classical solution concepts we investigate is Nash equilibrium. In particular, we show that no pure Nash equilibrium exists among the actors, and further illustrate that even “mixed Nash equilibrium" may not be achievable in the road pricing game. The paper also demonstrates the type of coalitions that are not only reachable, but also stable and profitable for the actors involved.
Abstract: This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler-s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game-s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result.