Search Results (11)

We build two multiple-stage game-theoretical models to capture how a ride-hailing platform’s ex-ante and ex-post pricing strategies induce show-up drivers’ strategic inter-area relocations. In both models, the platform operates its ride-hailing service in a two-area city, where the realizations of ride-hailing demand and supply are spatially asynchronous. Based on the subgame perfect equilibria, we show that show-up drivers’ relocation equilibria induced by the platform’s pricing strategy are not unique but that the equilibrium multiplicity does not affect the platform’s profit. Further, we find that the commission rate has non-monotonic discontinuous impacts on the platform’s profitability, drivers’ welfare, and pollutant emission under both pricing strategies. The continuous impact of an increase in the commission rate leads to a win–loss outcome for the platform and drivers without any effect on the environment, while the jumps result in a loss–win–win outcome for the platform, drivers, and the environment. We finally reveal that, relative to the ex-ante pricing strategy, the ex-post pricing strategy always benefits the platform at the cost of environmental pollution and enhances (reduces) drivers’ welfare when the relocation cost is sufficiently low (high). Managerial insights are also discussed. Full article

In contemporary mobile communications markets, various agents or players interact to pursue welfare. Regulatory policies enacted by governments in certain markets aim to maximize social welfare. However, some countries, both least developed and developing, often adopt successful models from developed nations without local market validation. Therefore, network economics serves as a pertinent framework for analyzing such policies. This paper introduces a novel scheme based on constrained optimization problems, where the constraints represent multilevel economic game equilibria within a system model involving three agents: the central planner, the mobile network operator, and the mobile data users. These agents strategically optimize their payoff functions by considering benefit factors and decision variables such as the subsidization factor, pricing, and data consumption. To this end, a three-stage dynamic game is proposed to model the players’ interactions, employing the backward induction method to ascertain the subgame perfect equilibrium from the Nash equilibrium. A case study is presented, demonstrating a 31.16% increase in social welfare between scenarios involving no adoption of the subsidization factor and its adoption at the optimal value when the central planner enacts it to other players in the game, even if they do not necessarily attain maximum payoff values. In countries aligning with this proposed model, social welfare is maximized through a subsidization scheme. Full article

We study a multi-objective finite-horizon game model of renewable, common resource extraction where the players have two separate objectives (one is economic success; the other describes the players’ environmental concern). We derive the cooperative strategy and the subgame-perfect Pareto equilibrium in linear-state non-stationary feedback strategies by employing the dynamic programming approach. Since the utility is transferable only based on the economic criterion, we need to revise the concept of time consistency and the payoff-distribution procedure to provide a mechanism for sustainable long-term cooperation. All the results are illustrated with a numerical example. Full article

In the much-studied Centipede Game, which resembles the Iterated Prisoners’ Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even though continuing play can benefit both players—but not if the rival defects immediately, which it has an incentive to do. We show that, without changing the structure of the game, interchanging the payoffs of the two players provides each with an incentive to cooperate whenever its turn comes up. The Nash equilibrium in the transformed Centipede Game, called the Reciprocity Game, is unique—unlike the Centipede Game, wherein there are several Nash equilibria. The Reciprocity Game can be implemented noncooperatively by adding, at the start of the Centipede Game, a move to exchange payoffs, which it is rational for the players to choose. What this interchange signifies, and its application to transforming an arms race into an arms-control treaty, are discussed. Full article

We design a mechanism of the players’ sustainable cooperation in multistage n-person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players’ rank based (PRB) algorithm for choosing a unique cooperative strategy profile and prove that corresponding optimal bundle of cooperative strategies satisfies time consistency, that is, at every subgame along the optimal game evolution a part of each original cooperative trajectory belongs to the subgame optimal bundle. We propose a refinement of the backwards induction procedure based on the players’ attitude vectors to find a unique subgame perfect equilibrium and use this algorithm to calculate a characteristic function. Finally, to ensure the sustainability of the cooperative agreement in a multistage game we employ the imputation distribution procedure (IDP) based approach, that is, we design an appropriate payment schedule to redistribute each player’s optimal payoff along the optimal bundle of cooperative trajectories. We extend the subgame consistency notion to extensive-form games with chance moves and prove that incremental IDP satisfies subgame consistency, subgame efficiency and balance condition. An example of a 3-person multistage game is provided to illustrate the proposed cooperation mechanism. Full article

We study a CSMA/CA (Carrier Sense Medium Access with Collision Avoidance) wireless network where some stations deviate from the defined contention mechanism. By using Bianchi’s model, we study how this deviation impacts the network throughput and show that the fairness of the network is seriously affected, as the stations that deviate achieve a larger share of the resources than the rest of stations. Previously, we modeled this situation using a static game and now, we use repeated games, which, by means of the Folk theorem, allow all players to have better outcomes. We provide analytical solutions to this game for the two player case using subgame perfect and correlated equilibria concepts. We also propose a distributed algorithm based on communicating candidate equilibrium points for learning the equilibria of this game for an arbitrary number of players. We validate approach using numerical simulations, which allows comparing the solutions we propose and discussing the advantages of using each of the methods we propose. Full article

I introduce axiomatically infinite sequential games that extend Kuhn’s classical framework. Infinite games allow for (a) imperfect information, (b) an infinite horizon, and (c) infinite action sets. A generalized backward induction (GBI) procedure is defined for all such games over the roots of subgames. A strategy profile that survives backward pruning is called a backward induction solution (BIS). The main result of this paper finds that, similar to finite games of perfect information, the sets of BIS and subgame perfect equilibria (SPE) coincide for both pure strategies and for behavioral strategies that satisfy the conditions of finite support and finite crossing. Additionally, I discuss five examples of well-known games and political economy models that can be solved with GBI but not classic backward induction (BI). The contributions of this paper include (a) the axiomatization of a class of infinite games, (b) the extension of backward induction to infinite games, and (c) the proof that BIS and SPEs are identical for infinite games. Full article

This paper examines the subgame-perfect equilibria in symmetric $2\times 2$ supergames. We solve the smallest discount factor value for which the players obtain all the feasible and individually rational payoffs as equilibrium payoffs. We show that the critical discount factor values are not that high in many games and they generally depend on how large the payoff set is compared to the set of feasible payoffs. We analyze how the stage-game payoffs affect the required level of patience and organize the games into groups based on similar behavior. We study how the different strategies affect the set of equilibria by comparing pure, mixed and correlated strategies. This helps us understand better how discounting affects the set of equilibria and we can identify the games where extreme patience is required and the type of payoffs that are difficult to obtain. We also observe discontinuities in the critical values, which means that small changes in the stage-game payoffs may affect dramatically the equilibrium payoffs. Full article

This paper examines how to construct subgame-perfect mixed-strategy equilibria in discounted repeated games with perfect monitoring. We introduce a relatively simple class of strategy profiles that are easy to compute and may give rise to a large set of equilibrium payoffs. These sets are called self-supporting sets, since the set itself provides the continuation payoffs that are required to support the equilibrium strategies. Moreover, the corresponding strategies are simple as the players face the same augmented game on each round but they play different mixed actions after each realized pure-action profile. We find that certain payoffs can be obtained in equilibrium with much lower discount factor values compared to pure strategies. The theory and the concepts are illustrated in 2 × 2 games. Full article

We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner’s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games. Full article

We auction scarce rights to play the Proposer and Responder positions in ultimatum games. As a control treatment, we randomly allocate these rights and charge exogenous participation fees. These participation fee sequences match the auction price sequence from a session of the original treatment. With endogenous selection via auctions, we find that play converges to a session-specific Nash equilibrium, and auction prices emerge supporting this equilibrium by the principle of forward induction. With random assignment, we find play also converges to a session-specific Nash equilibrium as predicted by the principle of loss avoidance. While Nash equilibria with low offers are observed, the subgame perfect Nash equilibrium never is. Full article