Efficient equilibria in a differential game of capitalism

One considers a differential game of capitalism ‘à la Lancaster’. Feedback Nash equilibria and Pareto optimal solutions are characterized under the assumption that the planning horizon is infinite. It is then shown that, by combining a Pareto optimal solution with the Nash feedback equilibrium strategy pair, which plays the role of a threat, one can obtain an efficient equilibrium which is also subgame perfect in the sense of Selten. This result modifies sensibly the previous interpretation of the inherent inefficiency of capitalism.     

A stochastic differential game of capitalism

We develop a stochastic differential game of capitalism to analyze the role of uncertainty. In the deterministic game, the firm’s rent is completely taxed away and the firm stops investing completely. In the stochastic game, the government does not tax the firm’s rent completely. The firm posts a positive rate of investment if the firm’s rent exceeds the labor’s income. Although the cooperative solution is indeterminate, cooperation is always Pareto optimal compared to the non-cooperative Markovian Nash equilibrium. For individual rationality, we apply a payoff distribution procedure based on Yeung and Petrosyan (2006) to derive a subgame-consistent solution.     

On the dominance of capitalists leadership in a ‘Feedback-Stackelberg’ solution of a differential game model of capitalism

This paper deals with a modified version of the Lancaster model of capitalism, where it is assumed that there is a cost jointly borne by the two groups of players (workers versus capitalists) and associated with the bargaining of a larger share of consumption for the workers. It is shown that a Feedback- Stackelberg solution, with the capitalists acting as leaders and announcing their investment policy at the beginning of each period, is a solution dominating the Feedback-Nash solution. The paper is also intended to be a tutorial on the Feedback-Stackelberg solution, a concept not so often used by economic modelers.     

Optimality and consistency in a differential game with non-renewable resources

Imperfect competition amongst buyers for a non-renewable resource is modeled as a Stackelberg differential game. The buyers may act as a cartel or behave non-cooperatively in setting tariffs, which the sellers take as given. The buyer's optimal policy is not consistent when extraction costs depend on the stock level. Both optimal and consistent, unit and ad valorem tariff's are analyzed. When a buyers' cartel uses a consistent tariff, the sellers may prefer to behave as perfect competitors or a monopolist, depending on the functional form of demand and cost. Non-cooperative buyers who are constrained to act consistently are unable to extract any rent from competitive sellers.     

A differential game in a duopoly with instantaneous incentives

In this paper, we study a differential game in which two competing firms exploit a public renewable resource that is relevant from a landscape point of view. We consider a policy maker that provides an instantaneous incentive to the firms in order to prevent the resource exhaustion during the whole extraction period, which coincides with the harvesting license period. We compute an open-loop Nash equilibrium of the differential game, showing that it coincides with a linear feedback Nash equilibrium. Finally, we compute the value of the incentive that leads to the maximization of social welfare considering the incentive both as a pure transfer and as a cost.     

Buying cooperation in an asymmetric environmental differential game

We consider a two-player asymmetric differential game of pollution control. One player is non-vulnerable to pollution, or unwilling to consider damages when choosing her production policy in a non-cooperative game. We characterize the feedback-Nash equilibrium and the cooperative solution. We establish conditions under which the vulnerable player can buy the cooperation of the non-vulnerable player to control her emissions. We further use the Nash bargaining solution to allocate the total cooperative dividend between the two players and propose a time-consistent decomposition overtime of the total payoff.     

Existence of equilibrium in a differential game of spatial competition with advertising

We investigate a differential duopoly game with horizontal product differentiation and advertising efforts aimed at increasing market demand, to show that the standard approach to spatial competition fails to produce a pure-strategy price equilibrium in a dynamic game framework. This holds independently of the shape of the transportation cost function. Then, we introduce an endogenous cost associated with the choice of location and characterise the feedback equilibrium, identifying the necessary and sufficient condition for the existence of the pure-strategy (stationary) price equilibrium. The same condition is singled out for the static game where consumer population is constant. Finally, we show that the static game cannot be viewed as a special case of the dynamic one.     

Advertising a product to face a competitor entry: a differential game approach

We analyze a market in which advertising is the dominant marketing tool to create market share. We assume that an incumbent firm dominates the market during an initial stage, and that a new competitor is going to enter the market. In particular, we analyze the different advertising policies that the incumbent firm can adopt, before and after the entry of the rival. We explore three possible behaviours. In the first scenario the firm knows that the competitor will arrive at a given instant. In the second one we assume the original firm to be surprised, in the sense that it does not anticipate the entry of the opponent either because it does not expect the competitor to arrive, or it is not prepared to react before the entry takes place. Finally, in the third scenario, the original firm knows that the competitor will enter at a constant rate. We characterize a differential game model and compare the firms’ behaviours in a strategic perspective.     

The local stability of an open-loop Nash equilibrium in a finite horizon differential game

We propose a finite time differential game as a model for some economic processes and derive conditions for the Nash equilibrium solution to be locally asymptotically stable. We adopt the traditional ‘Cournot-reaction function’ notion of stability, which in our (continuous time) model becomes a function-to-function, or trajectory-to-trajectory, mapping. The conditions for stability seem to make economic sense. The equilibrium is less stable if the interaction terms in each period are large, if the game has a long duration, and if the discount rate is small.     

Fiscal and monetary policy co-ordination: A differential game approach

In this paper the interaction between the Treasury and the central bank is examined in the case of both cooperative and non-cooperative behaviour. Differential games are used in the framework of a continuous-time econometric model of the Italian economy. The Nash and the Stackelberg non-cooperative equilibrium solutions are computed, and the case for cooperation is analysed by considering the Nash and the Kalai-Smorodinsky bargaining models. It is shown that, in the Italian case, the government has a stronger bargaining position than the central bank. A comparison is then made between the different solutions to show that the drawbacks that emerge from non-cooperation are not simply those depending on the players' payoffs. Other features are in fact considered which constitute a further argument for policy co-ordination.     

Learning in a multilateral bargaining experiment

This paper analyzes data from an investigation of a majoritarian bargaining experiment. A learning model is proposed to account for the evolution of play in this experiment. It is also suggested that an adjustment must be made to account for the panel structure of the data. Such adjustments have been used in other fields and are known to be important as unadjusted standard errors may be severely biased downward. These results indicate that this adjustment also has an important effect in this application. Furthermore, an efficient estimator that takes into account heterogeneity across players is proposed. A unique learning model to account for the paths of play under two different amendment rules cannot be rejected with the standard estimator with adjusted standard errors, however it can be rejected using the efficient estimator. The data and the estimated learning model suggest that after proposing “fair” divisions, subjects adapt and their proposals change rapidly in the treatment where uneven proposals are almost always accepted. Their beliefs in the estimated learning model are influenced by more than just the most recent outcomes.     

Inequality and capitalism

By participation in lotteries, people reject the goals of equality of outcome or of opportunity - fortunately because both are infeasible.     

Productivity bargaining: a reassessment

While governments tend to regard productivity bargaining as a long term anti-inflationary weapon, the author's research points out its weaknesses in this direction, and indicates that productivity bargaining may ultimately have far more important effects on the structural and behavioural development of collective bargaining at plant level.     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

Optimal control and differential game models of military expenditure in less developed countries

This paper presents optimal control and differential game models of military expenditure in less developed countries. We emphasise the strategic interconnections between aggressive neighbours and explicitly stress the optimal resource allocation problem between civilian and military expenditure. A major innovation of the analysis is to analyse the asymmetric reaction functions of the two agents and the formalisation of the stylised fact that most LDC arms races have taken place between participants of ‘unequal’ size.     

Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model

Fershtman and Nitzan (Eur. Econ. Rev. 35:1057–1067, 1991) presented a continuous dynamic public good game and solved the model for feedback Nash equilibria. Wirl (Eur. J. Polit. Econ. 12:555–560, 1996) extended the model and considered nonlinear strategies. Both models do not include uncertainty and hence neglect an important factor in the theory of public goods. We extend the framework of Nitzan and Fershtman and include a diffusion term. We consider two cases. In the first case, the volatility of the diffusion term is dependent on the current level of the public good. This set-up will in principle lead to the same type of feedback strategies computed under certainty. In the second case, the volatility is dependent on the current rate of public good provision by the agents. The results are qualitatively different. We provide a detailed discussion as well as numerical examples. In particular, we show that in both cases uncertainty signifies the free rider effect.     

Rebates in a Bertrand game

We study a price competition game in which customers are heterogeneous in the rebates they get from either of two firms. We characterize the transition between competitive pricing (without rebates), mixed strategy equilibrium (for intermediate rebates), and monopoly pricing (for larger rebates).     

Categorization and correlation in a random-matching game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player i is a best response to the distribution of strategies of his opponents (when they face i) in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.     

Plant-level bargaining in France

Institutionalised bargaining and formal collective agreements at plant level are a rarity in France. However, research shows that some form of unofficial bargaining does take place. Edward Slack illustrates this phenomenon using evidence obtained from a chemical plant and an industrialised dairy in 1974.