Browsing by Subject "Dynamic games"

Now showing 1 - 4 of 4

Open Access
Consensus as a Nash equilibrium of a dynamic game
(IEEE, 2016) Niazi, Muhammad Umar B.; Özgüler, Arif Bülent; Yıldız, Aykut
Consensus formation in a social network is modeled by a dynamic game of a prescribed duration played by members of the network. Each member independently minimizes a cost function that represents his/her motive. An integral cost function penalizes a member's differences of opinion from the others as well as from his/her own initial opinion, weighted by influence and stubbornness parameters. Each member uses its rate of change of opinion as a control input. This defines a dynamic non-cooperative game that turns out to have a unique Nash equilibrium. Analytic explicit expressions are derived for the opinion trajectory of each member for two representative cases obtained by suitable assumptions on the graph topology of the network. These trajectories are then examined under different assumptions on the relative sizes of the influence and stubbornness parameters that appear in the cost functions.
Open Access
Foraging motion of swarms as nash equilibria of differential games
(2016-09) Yıldız, Aykut
The question of whether foraging swarms can form as a result of a non-cooperative game played by individuals is shown here to have an affirmative answer. A dynamic (or, differential) game played by N agents in one-dimensional motion is introduced and models, for instance, a foraging ant colony. Each agent controls its velocity to minimize its total work done in a finite time interval. The agents in the game start from a set of initial positions and migrate towards a target foraging location. Such swarm games are shown to have unique Nash equilibra under two different foraging location specifications and both equilibria display many features of a foraging swarm behavior observed in biological swarms. Explicit expressions are derived for pairwise distances between individuals of the swarm, swarm size, and swarm center location during foraging. Foraging swarms in one-dimensional motion with four different information structures are studied. These are complete and partial information structures, hierarchical leadership and one leader structures. In the complete information structure, every agent observes its distance to every other agent and makes use of this information in its effort optimization. In partial information structure, the agents know the position of only its neighboring agents. In the hierarchical leadership structure, the agents look only forward and measures its distance to the agents ahead. In single leader structure, the agents know the position of only leader. In all cases, a Nash equilibrium exists under some realistic assumptions on the sizes of the weighing parameters in the cost functions. The consequences of having a “passive” leader in a swarm are also investigated. We model foraging swarms with leader and followers again as non-cooperative, multi-agent differential games. We consider two types of leadership structures, namely, hierarchical leadership and a single leader structure. In both games, the type of leadership is assumed to be passive since a leader is singled out only due to its rank in the initial queue. We identify the realistic assumptions under which a unique Nash equilibrium exists in each game and derive the properties of the Nash equilibriums in detail. It is shown that having a passive leader economizes in the total information exchange at the expense of aggregation stability in a swarm.
Open Access
A genetic game of trade, growth and externalities
(1997) Özyıldırım, Süheyla
This dissertation introduces a new adaptive search algorithm, Genetic Algorithm (GA), for dynamic game applications. Since GAs require little knowledge of the problem itself, computations based on these algorithms are very attractive for optimizing complex dynamic structures. Part one discusses GA in general, and dynamic game applications in particular. Part two is comprised of three essays on computational economics. In Chapter one, a genetic algorithm is developed to approximate open-loop Nash equilibria in non-linear difference games of fixed duration. Two sample problems are provided to verify the success of the algorithm. Chapter two covers discrete-time dynamic games with more than two conflicting parties. In games with more than two players, there arises the possibility of coalitions among groups of players. A three-country, two-bloc trade model analyzes the impact of coalition formation on optimal policies. Chapter three extends GA further to solve open-loop differential games of infinite duration. In a dynamic North/South trade game with transboundary knowledge spillover and local pollution optimal policies are searched. Cooperative and noncooperative modes of behavior are considered to address the welfare effects of pollution and knowledge externalities.
Open Access
Multi-player race
(Elsevier B.V., 2018) Doğan, S.; Karagözoğlu, Emin; Keskin, K.; Sağlam, Ç.
We present a model of race with multiple players and study players’ effort choices and expected prizes in equilibrium. We show that, in equilibrium, once any two players win one battle each, the remaining players do not exert any effort anymore. This turns the continuation game into a two-player race. This is different than the results in previous two-player models of race, which report that all states of the game are reached with positive probabilities. We also provide a set of comparative static results on the effects of the number of players and the victory threshold.