The Stackelberg Games of Water Extraction with Myopic Agents

We consider a discrete-time, infinite-horizon dynamic game of groundwater extraction. A Water Agency charges an extraction cost to water users and controls the marginal extraction cost so that it depends not only on the level of groundwater but also on total water extraction (through a parameter [Formula: see text] that represents the degree of strategic interactions between water users) and on rainfall (through parameter [Formula: see text]). The water users are selfish and myopic, and the goal of the agency is to give them incentives so as to improve their total discounted welfare. We look at this problem in several situations. In the first situation, the parameters [Formula: see text] and [Formula: see text] are considered to be fixed over time. The first result shows that when the Water Agency is patient (the discount factor tends to 1), the optimal marginal extraction cost asks for strategic interactions between agents. The contrary holds for a discount factor near 0. In a second situation, we look at the dynamic Stackelberg game where the Agency decides at each time what cost parameter they must announce. We study theoretically and numerically the solution to this problem. Simulations illustrate the possibility that threshold policies are good candidates for optimal policies.

Strong Time-Consistency of a Core: An Application to the Pollution Control Problem in Eastern Siberia

In this paper, we study the (strong) time-consistency property of the core for a linear-quadratic differential game of pollution control with nonzero absorption coefficient and real values of the model parameters. The values of parameters are evaluated based on the data for the largest aluminum enterprises of Eastern Siberia region of the Russian Federation for the year 2016. The obtained results are accompanied with illustrations.

The Polymatrix Gap Conjecture

This paper proposes a novel way to compare classes of strategic games based on their sets of pure Nash equilibria. This approach is then used to relate the classes of zero-sum games, polymatrix, and k-polymatrix games. This paper concludes with a conjecture that k-polymatrix games form an increasing chain of classes.

Wage Bargaining and Minimum Wages in a Search–Matching Model

In this paper, we analyze the introduction of a nonbinding minimum wage in a search–matching model with wage bargaining. Applying the Kalai–Smorodinsky bargaining solution instead of the commonly applied Nash solution, we provide a theoretical explanation for spillover effects of minimum wages on other wages higher up in the wage distribution. The labor market equilibrium in the Kalai–Smorodinsky solution with a minimum wage is characterized by lower market tightness, a higher unemployment rate, and lower vacancy rate than the equilibrium in the Nash solution. Moreover, we show that a nonbinding minimum wage can increase social welfare.

A Stackelberg–Nash–Cournot Equilibrium in a Pollution Reduction Scheme

This paper presents a Stochastic Stackelberg–Nash–Cournot Equilibrium model with continuous market demand distribution to examine the effectiveness of ambient charges as an effective policy measure for reducing nonpoint source pollution in a hybrid scheme. To do so, we consider the supply side of an energy market with hybrid technology that competes in an oligopoly market setting. Within such a setting, each power plant or firm uses a mix of fossil fuels (F) and renewable energy sources (R) to generate power at any given time. The demand for electricity is not realized at the time when the firm (leader) makes the decision. The competition between the two energy sources available to leader is assumed to be of Nash–Cournot equilibria, implying that they use one energy source to generate electricity, whilst holding the other energy source as a constant when the followers reactions are known. Based on the assumption that the demand function is affine and power plants cost functions are quadratic, we obtain the Stackelberg–Nash–Cournot equilibrium. Hence, our analysis provides an interesting insight into the effectiveness of using ambient charges, within the context of a Stochastic Stackelberg–Nash–Cournot competition, as an environmental economic policy measure when included within a robust hybrid scheme. From an economical point of view, this allows pollutants to develop specific control technologies by undertaking research and development (R&D) measures or production processes to maintain emissions standards in a hybrid scheme. From a policy implementations point of view, the environmental authority can use the pollution abatement technology ratio to set ambient charges and industry specific pollutant quantitative limits subject to technological variations.

An OLG Differential Game of Pollution Control with the Risk of a Catastrophic Climate Change

This paper studies an overlapping generations (OLG) differential game on optimal emissions with continuous age structure and different types of individuals. At the (stochastic) arrival of a catastrophic climate change, the utility and the damage to the stock of pollution change for the rest of the time horizon. We derive the open-loop (OL) Nash equilibrium and show that it is subgame perfect and moreover equal to the feedback Stackelberg one. We compare the solution to the cooperative one (using the social welfare as objective function) and show the different dynamic evolutions of optimal emissions over time. Finally, we derive a time-consistent tax scheme that reaches the cooperative optimal solution in the OL Nash equilibrium. The tax scheme turns out to be heterogeneous with respect to age and type (anticipating and nonanticipating the catastrophic climate change). Setting taxes that are homogeneous across the individual type leads to an OL Nash solution that produces socially optimal total emissions, but lower individual utilities.

Dynamic Bargaining and Time-Consistency in Linear-State and Homogeneous Linear-Quadratic Cooperative Differential Games

Three different solution concepts are reviewed and computed for linear-state and homogeneous linear-quadratic cooperative differential games with asymmetric players. Discount rates can be nonconstant and/or different. Special attention is paid to the issues of time-consistency, agreeability and subgame-perfectness, both from the viewpoint of sustainability of cooperation and from the credibility of the announced equilibrium strategies.

Delegation Using Forward Induction

This paper explores how delegation can be used as a signal to sustain cooperation. I consider a static principal–agent model with two tasks, one resembling a coordination game. If there is asymmetric information about the agent’s type, the principal with high private belief can delegate the first task as a signal. This is also supported by the forward induction argument. However, in the laboratory setting, this equilibrium is chosen only sometimes. When the subjects have information about past sessions, there is a significant increase in the use of delegation. This finding sheds light on equilibrium selection in Bayesian games.

Generating Empirical Core Size Distributions of Hedonic Games Using a Monte Carlo Method

Hedonic games have gained popularity over the last two decades, leading to several research articles that have used analytical methods to understand their properties better. In this paper, a Monte Carlo method, a numerical approach, is used instead. Our method includes a technique for representing, and generating, random hedonic games. We were able to create and solve, using core stability, millions of hedonic games with up to 16 players. Empirical distributions of the hedonic games’ core sizes were generated, using our results, and analyzed for games of up to 13 players. Results from games of 14–16 players were used to validate our research findings. Our results indicate that core partition size might follow the gamma distribution for games with a large number of players.

Nash Equilibrium Points for Generalized Matrix Game Model with Interval Payoffs

Game theory-based models are widely used to solve multiple competitive problems such as oligopolistic competitions, marketing of new products, promotion of existing products competitions, and election presage. The payoffs of these competitive models have been conventionally considered as deterministic. However, these payoffs have ambiguity due to the uncertainty in the data sets. Interval analysis-based approaches are found to be efficient to tackle such uncertainty in data sets. In these approaches, the payoffs of the game model lie in some closed interval, which are estimated by previous information. The present paper considers a multiple player game model in which payoffs are uncertain and varies in a closed intervals. The necessary and sufficient conditions are explained to discuss the existence of Nash equilibrium point of such game models. Moreover, Nash equilibrium point of the model is obtained by solving a crisp bi-linear optimization problem. The developed methodology is further applied for obtaining the possible optimal strategy to win the parliament election presage problem.