Browsing by Subject "Nash Equilibrium"

Now showing 1 - 4 of 4

Open Access
Centralized and decentralized management of water resources with multiple users
(2011) Saleh, Yahya
In this study, we investigate two water inventory management schemes with multiple users in a dynamic game-theoretic structure over a two-period planning horizon. We first investigate the groundwater inventory management problem (i) under the decentralized management scheme, where each user is allowed to pump water from a common aquifer making usage decisions individually in a noncooperative fashion, and (ii) under the centralized management scheme, where users are allowed to pump water from a common aquifer with the supervision of a social planner. We consider the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider different geometric configurations overlying the aquifer, namely, the strip, ring, double-layer ring, multi-layer ring and grid configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed. We then consider the surface and groundwater conjunctive use management problem with two non-identical users in a dynamic game-theoretic structure over a planning horizon of two periods. Optimal water allocation and usage policies are obtained for each user in each period under the decentralized and centralized settings. Some pertinent hypothetical numerical examples are also provided.
Open Access
Delegation in a duopolistic differentiated goods market with Cournot competition
(1995) Ünver, Mustafa Utku
We consider the impact of delegation in a Cournotic duopoly with differentiated goods upon the firms’ profit maximization behavior. In an oligopoly, delegation in each firm can be modeled through a specific non-cooperative game. Delegation games in a differentiated goods market with affine demand are studied within the Cournot competition concept where redelegation is permitted in a symmetric duopoly. The following results are demonstrated: The maximand delegated by each primary delegator, i.e. owner of each firm, converges in monotonically decreasing fashion to the true profit function in the absence of delegation costs, and total industry output at the Cournot equilibrium converges in monotonically increasing fashion to some output level. Welfare changes due to redelegation are also considered.
Open Access
Non-cooperative game theory under prospect theory
(2016-05) Keskin, Kerim
This dissertation consists of three essays in which I study prospect theory preferences in non-cooperative game-theoretic frameworks. In decision-making experiments, it is commonly observed that actual choice behavior might violate the axioms of expected utility theory (EUT). Kahneman and Tversky (1979) argue that such experimental findings invalidate EUT as a descriptive model and propose prospect theory as an alternative representation of preferences. Later, Tversky and Kahneman (1992) propose cumulative prospect theory (CPT). Both of these theories stipulate that individual preferences can be represented by a pair of functions: probability weighting function and value function. These functions capture three key aspects of the theory: subjective probability weighting, reference dependence, and loss aversion. In the first essay of this dissertation, I study mixed strategy equilibrium for finite normal form games in which agents' preferences are represented by the pair of functions suggested in CPT. I introduce the notion of CPT equilibrium, prove the existence of CPT equilibrium for finite normal form games, and analyze the set of CPT equilibria for some normal form games. In the second essay, I study correlated equilibrium for finite normal form games in which agents' preferences are represented by the same pair of functions. I relate the notion of correlated CPT equilibrium to the notion of CPT equilibrium and investigate the differences between the sets of correlated equilibria under EUT and CPT preferences. Finally, in the third essay, I study a first-price sealed-bid auction. I concentrate on subjective probability weighting and analyze overbidding behavior which is commonly observed in first-price auction experiments. I show that inverse S-shaped probability weighting functions cannot completely explain overbidding and that such functions can provide a partial explanation for bidders with high valuations. Keywords: Correlated Equilibrium, First-price Sealed-bid Auctions, Mixed Strategy Equilibrium, Nash Equilibrium, Prospect Theory.
Open Access
Power allocation strategies for channel switching and wireless localization
(2018-08) Sezer, Ahmet Dündar
Optimal power allocation is an important approach for enhancing performance of both communication and localization systems. In this dissertation, optimal channel switching problems are investigated for average capacity maximization via optimization of power resources in general. In addition, power control games are designed for a wireless localization network including anchor and jammer nodes which compete for the localization performance of target nodes. First, an optimal channel switching strategy is proposed for average capacity maximization in the presence of average and peak power constraints. Necessary and sufficient conditions are derived in order to determine when the proposed optimal channel switching strategy can or cannot outperform the optimal single channel strategy, which performs no channel switching. Also, it is obtained that the optimal channel switching strategy can be realized by channel switching between at most two different channels. In addition, a low-complexity optimization problem is derived in order to obtain the optimal channel switching strategy. Furthermore, based on some necessary conditions that need to be satisfied by the optimal channel switching solution, an alternative approach is proposed for calculating the optimal channel switching strategy. Second, the optimal channel switching problem is studied for average capacity maximization in the presence of additive white Gaussian noise channels and channel switching delays. Initially, an optimization problem is formulated for the maximization of the average channel capacity considering channel switching delays and constraints on average and peak powers. Then, an equivalent optimization problem is obtained to facilitate theoretical investigations. The optimal strategy is derived and the corresponding average capacity is specified when channel switching is performed among a given number of channels. Based on this result, it is shown that channel switching among more than two different channels is not optimal. In addition, the maximum average capacity achieved by the optimal channel switching strategy is formulated as a function of the channel switching delay parameter and the average and peak power limits. Then, scenarios under which the optimal strategy corresponds to the exclusive use of a single channel or to channel switching between two channels are described. Furthermore, sufficient conditions are obtained to determine when the optimal single channel strategy outperforms the optimal channel switching strategy. Third, the optimal channel switching problem is studied for average capacity maximization in the presence of multiple receivers in the communication system. At the beginning, the optimal channel switching problem is proposed for average capacity maximization of the communication between the transmitter and the secondary receiver while fulfilling the minimum average capacity requirement of the primary receiver and considering the average and peak power constraints. Then, an alternative equivalent optimization problem is provided and it is shown that the solution of this optimization problem satisfies the constraints with equality. Based on the alternative optimization problem, it is obtained that the optimal channel switching strategy employs at most three communication links in the presence of multiple available channels in the system. In addition, the optimal strategies are specified in terms of the number of channels employed by the transmitter to communicate with the primary and secondary receivers. Last, a game theoretic framework is proposed for wireless localization networks that operate in the presence of jammer nodes. In particular, power control games between anchor and jammer nodes are designed for a wireless localization network in which each target node estimates its position based on received signals from anchor nodes while jammer nodes aim to reduce localization performance of target nodes. Two different games are formulated for the considered wireless localization network: In the first game, the average Cram´er-Rao lower bound (CRLB) of the target nodes is considered as the performance metric, and it is shown that at least one pure strategy Nash equilibrium exists in the power control game. Also, a method is presented to identify the pure strategy Nash equilibrium, and a sufficient condition is obtained to resolve the uniqueness of the pure Nash equilibrium. In the second game, the worst-case CRLBs for the anchor and jammer nodes are considered, and it is shown that the game admits at least one pure Nash equilibrium.