Pareto Dominant Nash Equilibrium Research Articles

A Conceptual Analysis of Equilibrium Bidding Strategy in a Combined Oligopoly and Oligopsony Wholesale Electricity Market

This paper proposes a semi-analytical method to obtain the equilibrium bidding strategies for generation and demand units in a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">combined</i> oligopoly and oligopsony wholesale electricity market. Such market structure is the outcome of the increasing deployment of demand response programs that facilitate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">active participation of demand-side players</i> in the price-setting process. In this analysis, the concept of supply function equilibrium (SFE) is used to investigate the oligopolistic competition among generation units. The SFE model is extended and the demand function equilibrium (DFE) is obtained to study the oligopsonistic competition among demand units. The economic behavior of a market participant is formulated as a bi-level programming (BLP) problem. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">imperfect competition</i> among generation units, as well as among demand units, are modeled as a non-cooperative game. Next, a direct method is developed to calculate all candidate equilibriums of the market, and the locational marginal prices (LMPs) in terms of the bidding strategies of the market participants. The BLP problem is solved by obtaining the coordinated Pareto-dominant Nash equilibrium of the market participants’ non-cooperative games. Finally, the proposed analysis is examined in case studies. Accordingly, we report <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">insightful observations</i> with respect to the impact of the changes in the new market structure, at firm-level and market-level, such as in terms of mitigating market power of generation units, the market clearing prices and quantities, surplus for generation units and demand units, and potential impact on market efficiency.

On Asynchronicity of Moves and Coordination

This paper shows that asynchronicity of moves can lead to a unique prediction in coordination games, in an infinite-horizon setting, under certain conditions on off-equilibrium payoffs. In two-player games we derive necessary and sufficient conditions for play ultimately being absorbed in the Pareto dominant Nash equilibrium of the stage game, for every Markov perfect equilibrium. For players patient enough, the condition is that the Pareto dominant Nash equilibrium is also risk dominant, but for lower levels of patience the condition departs from simple risk-dominance. For general n-player symmetric games with patient players, we show that a necessary and sufficient condition for the Pareto dominant Nash equilibrium to be the unique limit outcome in all symmetric Markov perfect equilibrium is a particular generalization of risk-dominance for more than two players. We provide extensions to the unique selection results to all subgame perfect Nash equilibria, and to coordination games in which different players prefer different Nash equilibria of the stage game.

Endogenous Movement and Equilibrium Selection in Spatial Coordination Games

We study the effects of agent movement on equilibrium selection in network based spatial coordination games with Pareto dominant and risk dominant Nash equilibria. Our primary interest is in understanding how endogenous partner selection on networks influences equilibrium selection in games with multiple equilibria. We use agent based models and best response behaviors of agents to study our questions of interest. In general, we find that allowing agents to move and choose new game play partners greatly increases the probability of attaining the Pareto dominant Nash equilibrium in coordination games. We also find that agent diversity increases the ability of agents to attain larger payoffs on average.

Strategic loan defaults and coordination: An experimental analysis

This paper experimentally studies the impact of bank and borrower fundamentals on loan repayment. We find that solvent borrowers are more likely to default strategically when the bank’s expected strength is low, although loan repayment is a Pareto dominant Nash equilibrium. Borrowers are also less likely to repay when other borrowers’ expected repayment capacity is low, regardless of banks’ fundamentals. We show that changes in expectations about bank and borrower fundamentals change the risk dominance properties of the borrowers’ coordination problem, and that these changes subsequently explain strategic defaults. For the individual borrower, loss aversion and negative past experiences reduce repayment, suggesting that bank failure can be contagious in times of distress.

Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism

Empirical and experimental evidence suggests different levels of sophistication among families in the Boston Public School student assignment plan. We analyze the preference revelation game induced by the Boston mechanism with sincere players who report their true preferences and sophisticated players who play a best response. We characterize the set of Nash equilibrium outcomes as the set of stable matchings of a modified economy, where sincere students lose priority to sophisticated students. Any sophisticated student weakly prefers her assignment under the Pareto-dominant Nash equilibrium of the Boston mechanism to her assignment under the recently adopted student-optimal stable mechanism. (JEL D82, I21)

Random access game in ad hoc networks with cooperative and noncooperative users

Motivated by the fact that the exponential back-off algorithm is unfair towards nodes in the middle of networks, we propose two approaches to computing the optimal persistence probabilities in Medium Access Control based on game theory. The first is a cooperative game theoretic MAC with the objective of total payoff maximisation. By decomposing the overall problem into each user's subproblem, we solve the nonconvex random access problem in a distributed manner. The existence, uniqueness and stability of the Nash Equilibrium (NE) for the cooperative game are proved. The second is the noncooperative persistence scheme with an aim to minimise information exchanging among nodes. This formulation leads to a simple iterative scheme by which each user can arrive at a Pareto dominant NE. Simulation results illustrate the performance of these algorithms.

Customer relationship management in competitive environments: The positive implications of a short-term focus

Researchers and business thought leaders have emphasized that firms must think and act with a long-term horizon when managing customer relationships. We demonstrate that, in contrast to this widely held view, profits in competitive environments may be maximized when firms ignore the future and instead maximize period-by-period profits from customers. Intuitively, while a long-term focus yields more loyal customers, it greatly increases short-term price competition to gain and keep customers. Consequently, overall firm profits and customer lifetime value may be lower when firms directly maximize multi-period profits from customers. Specifically, we analyze a model with segment-level pricing where firms in a duopoly can choose between period-by-period and multi-period profit maximization and demonstrate that, in many cases, a symmetric focus on period-by-period profit maximization emerges as the Pareto-dominant Nash equilibrium. We extend the model in two directions. First, we demonstrate that this superiority of the short-term focus endures even when a revenue expansion effect applies—that is, when customer loyalty leads to enhanced revenues. Second, we examine the case where customers are strategic and incorporate the long-term implications of their choices into their decision-making. Here we demonstrate that it may pay for firms to be myopic even when customers are strategic. The focus on multi-period surplus makes customers less price sensitive to price variations at the early stage of the game. Consequently, the focus on maximizing period-by-period profits enables the firms to charge higher upfront prices and leverage this lower price sensitivity into higher profits. Overall, our results highlight the paradox that, when it comes to managing customer relationships in competitive environments, a short-term focus may constitute the optimal long-term strategy.

Does complexity reduce coordination?

Herein it is shown that increased complexity does not necessarily imply more coordination failure. Experienced people playing a 4-player spatial grid game with over 68 000 strategy choices and (68 000)4 potential outcomes were as likely to find the Pareto dominant Nash equilibrium as in a corresponding normal form game.

Private Sector Participation: A Theoretical Justification of the Brazilian Position

The Brazilian position on the issue of private sector participation in the efforts to forestall and resolve emerging markets crises is that there should be an approach of contacting and convincing a large number, but not the totality, of private creditors. They should be convinced that the international public sector loans will allow a transition to stability that is overfinanced in case they voluntarily join in by maintaining their exposure to the country, at the spreads they choose, and with the counterparts they wish to have as clients. We model private sector participation by means of a game. We show that the traditional argument that there is a coordination problem among the private creditors does not exist in a model without Knightian uncertainty, because there is a unique Pareto dominant Nash equilibrium that involves participation. By introducing Knightian uncertainty, we show that if the degree of uncertainty, as measured by the uncertainty aversion, is high enough, then there is a unique Nash equilibrium under uncertainty, which involves nonparticipation. Finally, we show that if there is a large enough number of private creditors who decrease their uncertainty aversion, then again private participation becomes the unique Pareto dominant Nash equilibrium under Knightian uncertainty. If we interpret the approach of contacting and convincing the private creditors as decreasing their uncertainty aversion, then this last result is a justification of the Brazilian position. In fact, the private creditors would voluntarily choose to maintain their exposures, because private sector participation is the unique Pareto dominant Nash equilibrium under uncertainty of the game.

Learning, Mutation, and Long Run Equilibria in Games

An evolutionary model with a finite number of players and with stochastic mutations is analyzed. The expansion and contraction of strategies is linked to their current relative success, but mutuation, perturbing the system from its deterministic evolution, are present as well. The focus is on the long run implications of ongoing mutations, which drastically reduce the set of equilibria. For 2 by 2 symmetric games with two symmetric strict Nash equilibria the risk dominant equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium. Copyright 1993 by The Econometric Society.

Communication in Coordination Games

We present experimental evidence on nonbinding, preplay communication in bilateral coordination games. To evaluate the effect of cheap talk, we consider two communication structures (one-way and two-way communication) and two types of coordination games (one with a cooperative strategy and a second in which one strategy is less risky). In games with a cooperative strategy, one-way communication increases play of the Pareto-dominant equilibrium relative to the no communication baseline; two-way communication does not always decrease the frequency of coordination failures. In the second type of game, two-way communication always leads to the Pareto-dominant Nash equilibrium, while one-way communication does not.