A Nikaido Isoda-Based Hybrid Genetic Algorithm and Relaxation Method for Finding Nash Equilibrium

Nash Equilibrium (NE) plays a crucial role in game theory. The relaxation method in conjunction with the Nikaido–Isoda (NI) function, namely the NI-based relaxation method, has been widely applied to the determination of NE. Genetic Algorithm (GA) with adaptive penalty is introduced and incorporated in the original NI-based relaxation method. The GA enhances the capability in the optimization step for computing the optimum response function. The optimization of the non-convex and non-concave NI function is made possible by GA. The proposed method thus combines the advantageous feature of the GA in its optimization capability and that of the relaxation method in its implementation simplicity together. The applicability of the method is shown through the illustrative examples, including the generalized Nash Equilibrium problem with nonlinear payoff functions and coupled constraints, the game with multiple strategic variables for individual players, and the non-differentiable payoff functions. All test example results suggest the appropriate crossover and mutation rate to be 0.05 and 0.002 for use in GA. These numbers are closed to the recommended values by DeJong. The proposed method shows its capability of finding correct NEs in all test examples.

A Monetary Incentive DTN Routing For Wireless Sensor Networks

The DTN (Delay/Interrupt Tolerant Network) protocol that relies on nodes to handle network interruptions is one of the important components of the wireless sensor network (WSN) routing protocol. However, due to resource consumption, nodes may be unable to unconditionally relay data. To address this issue, several incentive mechanisms have recently been proposed to encourage node participation. However, the existing solutions either do not fully consider the sender’s budget or do not consider the relay cost limitation, which violated the practical incentive mechanism requirements of the DTN protocol. In this paper, we focus on developing a new incentive mechanism for DTN routing that specifically address the challenges brought up by budget and relay cost limitation. Our core idea is to define the payoff functions of the sender and the next hops, then optimize the strategies under the constraints of the sender’s budget and the relay’s cost. Our experimental results demonstrate that the maximized social welfare for all participants can be realized under these constraints.

Combined Custom Hedging: Optimal Design, Noninsurable Exposure, and Operational Risk Management

Optimal Design of Combined Contingent Claims: Theory and Applications. In “Combined Custom Hedging: Optimal Design, Noninsurable Exposure, and Operational Risk Management”, Paolo Guiotto and Andrea Roncoroni develop a normative framework for the optimal design, value assessment, and operations management integration of financial derivatives. Most business and operating revenues entail a mix of financially insurable and noninsurable risk. A risk-averse firm may face them by positioning in a pair of financial derivatives with optimal bespoke payoff functions; one claim is written on the insurable term, and the other claim is written on any observable index exhibiting correlation to the noninsurable term. On a theoretical ground, the authors 1) state the problem in a general setup and prove existence and uniqueness of the optimal pair of combined claims, 2) show that the optimal payoff functions satisfy a Fredholm integral equation, and 3) assess the incremental benefit the firm obtains by switching from the optimal single-claim custom hedge to the optimal combined custom hedge they propose. On an experimental ground, they show that 1) the optimal combined custom hedge would be empirically relevant for a highly risk-averse firm facing a market shock shown during the first period of the COVID-19 pandemic in 2020, 2) integration with the optimal procurement in a generalized newsvendor model leads to a significant improvement in both risk and return, and: 3) this gain can be traded off for a substantial enhancement in operational flexibility.

Equilibrium uniqueness in aggregative games: very practical conditions

Various Nash equilibrium results for a broad class of aggregative games are presented. The main ones concern equilibrium uniqueness. The setting presupposes that each player has $$\mathbb {R}_+$$ R + as strategy set, makes smoothness assumptions but allows for a discontinuity of stand-alone payoff functions at 0; this possibility is especially important for various contest and oligopolistic games. Conditions are completely in terms of marginal reductions which may be considered as primitives of the game. For many games in the literature they can easily be checked. They automatically imply that conditional payoff functions are strictly quasi-concave. The results are proved by means of the Szidarovszky variant of the Selten–Szidarovszky technique. Their power is illustrated by reproducing quickly and improving upon various results for economic games.

Effects of Southwest Airlines on Carrier Profits and Entry Probabilities

This paper studies the effects of Southwest Airlines, the largest low-cost carrier (LCC) in the U.S., on other carriers’ payoff functions and entry probabilities. A static entry game model is developed and estimated by viewing entry as an indicator of underlying profitability and making use of Nash Equilibrium. Results indicate that Southwest has a remarkable and negative impact on the payoffs of other carriers. This impact is firm-specific, with LCCs being more affected than full-service carriers (FSCs). Comparing the two service types, the results show that Southwest’s nonstop presence apparently imposes more downward pressure on opponents’ profits than its connecting presence. A counterfactual experiment is then conducted. Once Southwest is counterfactually removed, the probability of each carrier entering a market significantly changes. This paper examines Southwest’s impacts from a new perspective and extends literature on entry game estimation.

Network Formation with Asymmetric Players and Chance Moves

We propose a model of network formation as a two-stage game with chance moves and players of various types. First, the leader suggests a connected communication network for the players to join. Second, nature selects a type vector for players based on the given probability distribution, and each player decides whether or not to join the network keeping in mind only his own type and the leader’s type. The game is of incomplete information since each player has only a belief over the payoff functions of others. As a result, the network is formed, and each player gets a payoff related to both the network structure and his type. We prove the existence of the Bayesian equilibrium and propose a new definition of the stable partially Bayesian equilibrium defining the network to be formed and prove its existence. The connection between the stable partially Bayesian equilibrium and the Nash equilibrium in the game is examined. Finally, we investigate the characteristics of the network structures under the stable partially Bayesian equilibrium in a three-player game with the major player as well as in the n-player game with a specific characteristic function.

Game Analysis of the Driving Modes in the Supply Chain Management Regarding Credit System Construction

This paper analyzes effort levels of supervisors, the manufacturers association and the administrative supervision department, and manufacturer in a supply chain management regarding credit system (CS) construction based on two different driving modes using game theory. A whole CS construction, in a supply chain management system, can be generally divided into two driving modes, industry regulation (IR), and administrative supervision (AS). The authors firstly establish payoff functions based on traditional income function and marginal effort-cost function. And then they analyze strategic equilibriums of the supervisors and the manufacturers based on their decision roles in the two modes. After that, they make comparisons on equilibrium states between IR and AS. From the results, they find that strategic equilibriums in AS construction is not necessarily better than those in IR construction. These results can also provide strategic help for CS construction in supply chain management when considering better combination between IR and AS.

Designing Strategic Games with Preestablished Nash Equilibrium through Artificial Inference and Global Learning

This work presents novel results obtained by the application of global optimization techniques to the design of finite, normal form games with mixed strategies. To that end, the Fuzzy ASA global optimization method is applied to several design examples of strategic games, demonstrating its effectiveness in obtaining payoff functions whose corresponding games present a previously established Nash equilibrium. In other words, the game designer becomes able to choose a convenient Nash equilibrium for a generic finite state strategic game and the proposed method computes payoff functions that will realize the desired equilibrium, making it possible for the players to reach the favorable conditions represented by the chosen equilibrium. Considering that game theory is a very useful approach for modeling interactions between competing agents and Nash equilibrium represents a powerful solution concept, it is natural to infer that the proposed method may be very useful for strategists in general. In summary, it is a genuine instance of artificial inference of payoff functions after a process of global machine learning, applied to their numerical components.

Drivers, Riders, and Service Providers: The Impact of the Sharing Economy on Mobility

It is widely believed that ride sharing, the practice of sharing a car such that more than one person travels in the car during a journey, has the potential to significantly reduce traffic by filling up cars more efficiently. We introduce a model in which individuals may share rides for a certain fee, paid by the rider(s) to the driver through a ride-sharing platform. Collective decision making is modeled as an anonymous nonatomic game with a finite set of strategies and payoff functions among individuals who are heterogeneous in their income. We examine how ride sharing is organized and how traffic and ownership are affected if a platform, which chooses the seat rental price to maximize either revenue or welfare, is introduced to a population. We find that the ratio of ownership to usage costs determines how ride sharing is organized. If this ratio is low, ride sharing is offered as a peer-to-peer (P2P) service, and if this ratio is high, ride sharing is offered as a business-to-customer (B2C) service. In the P2P case, rides are initiated by drivers only when the drivers need to fulfill their own transportation requirements. In the B2C case, cars are driven all the time by full-time drivers taking rides even if these are not motivated by their private needs. We show that, although the introduction of ride sharing may reduce car ownership, it can lead to an increase in traffic. We also show that traffic and ownership may increase as the ownership cost increases and that a revenue-maximizing platform might prefer a situation in which cars are driven with only a few seats occupied, causing high traffic. We contrast these results with those obtained for a social welfare-maximizing platform. This paper was accepted by Charles Corbett, operations management.