Welfare-Improving Effect of a Small Number of Followers in a Stackelberg Model

Abstract

We investigate a Stackelberg oligopoly model in which m leaders and $N - m$ followers compete. We find an important welfare effect that relates to anti-monopoly policies when we move from the Cournot model ($m = N$) to the Stackelberg model: Exchanging a small number of Cournot firms for Stackelberg followers always improves welfare under moderate conditions. This contrasts with the welfare effect that can reduce welfare when a small number of Cournot firms are exchanged for Stackelberg leaders. The key result behind this asymmetry is the contrasting limit results in the cases where m converges to N and m converges to 0. We also discuss the optimal number of leaders and the integer constraint for the number of firms.

Non‐fungible token‐based health record marketplace

“…Here, Equation ( 18) represents maximizing the timeaveraged reward over time duration T , and the constraint (19) ensures that the privacy index values of the selected data fields will not cross beyond the given I M constraint, where I D l represents the privacy index value of a specific data field D l . Equation (20) indicates that the selection variable S D l is a binary variable.…”

“…Stackelberg focuses on one seller being the leader and making the first move, while Cournot focuses on multiple sellers making the first move together. Also, the Stackelberg mechanism is proved to be more efficient than the Cournot equilibrium as to the relative efficiency of the two equilibria [20]. Bertrand assumes that all consumers purchase from the lowest‐price seller.…”

The Simulation of Oligopoly Information Equilibria with Agents' Capacity Constraints

“…The capacity limitations were considered in models with linear [20]- [22] and quadratic [23], [24] functions of agents costs in the symmetric Coumot oligopoly. The asymmetric capacitylimited oligopoly was investigated in the presence of the Stackelberg leader [12], [25]. The Pareto-effective solution was obtained [26] for the problem of unlimited agents actions choice for oligopoly market.…”

Game-theoretic analysis of Stackelberg oligopoly with arbitrary rank reflexive behavior of agents

“…The studies were carried out in the framework of the action game in the case of symmetric agent's awareness for the linear model of oligopoly (Karmarkar and Rajaram, 2012;Ledvina and Sigar, 2012;Currarini and Marini, 2013;Vasin, 2014) and also for the nonlinear model of oligopoly (Naimzada and Sbragia, 2006;Naimzada and Tramontana, 2015;Cavalli et al, 2015;Askar and Alnowibet, 2016), including the surveys (Jørgensen and Zaccour, 2014;Colacicco, 2015). The investigations of the oligopoly market with Stackelberg leadership (Ino and Matsumura, 2016;Peng et al, 2016), as a rule, were based on a priori defined positions of leader and follower. In addition, the problem of comparative analysis of the leader position and the follower position (Sherali, 1984;Boyer and Moreaux, 1987) created the research area of oligopoly market in case of leaders non-uniqueness (DeMiguel and Xu, 2009;Julien, 2017;Solis et al, 2017).…”