Stackelberg Leader-follower Game Research Articles

Option Premia in Acquisitions

In this paper we develop and test a theoretical framework that models the negotiation and timing processes of corporate acquisitions. The acquisition timing is modelled using real options techniques, and the negotiation process between target and bidder firms is assumed to be a Stackelberg (leader-follower) game with complete information. From the equilibrium strategies, we obtain testable implications for the determinants of the offer premia based on the characteristics of both the bidder and target firms. The three hypotheses related to acquisition premium are tested in a sample of 228 US target firms using an event study methodology and cross sectional regressions. Consistent with the predictions in the model, we find that target volatility and market to book ratios are important determinants of the offer premium. Our finding relating target volatility and target premium is important since this determinant does not emerge in existing models of takeovers.

OPTIMAL PRICING AND QUALITY CHOICE WHEN INVESTMENT IN QUALITY IS IRREVERSIBLE

This paper examines the price and quality choice of a single product, risk‐neutral monopolist who can delay irreversible investments required for market entry. It is shown that the price and quality she chooses at entry increase with uncertainty about the size of future demand. In a Stackelberg leader‐follower game, the leader and follower pre‐commit immediately up to a certain level of uncertainty. In this case the leader produces the higher quality good. When uncertainty is higher than this threshold, the follower will wait and enter the market later with a higher quality good.

A Bi-Level Non-Linear Multi-Objective Decision Making under Fuzziness

This paper studies a bi-level non-linear multi-objective decision making (BLN — MODM) problem with linear (or nonlinear) constraints, and in which the objective function at each levels are nonlinear functions, which are to be maximized. The BLN-MODM problem can be thought of as a static version of the Stackelberg leader-follower game in which a Stackelberg strategy is used by the leader (or the higher — level decision maker (HLDM)), given the rational reaction of the follower (or the lower-level decision maker (LLDM)). From this point of view, this paper proposes a two-planner bi-level multi-objective decision-making model and solution method for solving this problem. This method uses the concepts of tolerance membership function and multi-objective optimization (MOO) (at each level) to develop a fuzzy max — min decision model for generating Pareto optimal (satisfactory) solution for BLN — MODM problem. The HLDM specifies his/her objective functions and decisions with possible tolerances, which are described by membership functions of fuzzy set theory. Then, the LLDM uses this preference information for HLDM and solves his/her problem subject to the HLDMs’ restrictions. An illustrative numerical example is given to demonstrate the obtained results.

A global optimization method for nonlinear bilevel programming problems

Nonlinear two-level programming deals with optimization problems in which the constraint region is implicitly determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the nonlinear bilevel programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques.

Interactive bilevel multi-objective decision making

From a perspective of non-linear bilevel multi-objective decision-making problem (BMDMP) of the leader-follower Stackelberg game, this paper presents a two-person bilevel multi-objective decision-making model and an interactive algorithm for solving the problem. The algorithm simplifies a BMDMP by transforming it into separate multi-objective decision-making problems at the upper- and lower-levels, thereby avoiding the difficulty associated with non-convex mathematical programming to arrive at an optimal solution. In addition, the authors put forward the satisfactoriness concept as the upper level decision maker's preference. The algorithm facilitates the interactive nature of bilevel multi-objective decision making for non-inferior solutions. Thus, the algorithm provides a way to solve BMDMP.

A global optimization approach for the linear two-level program

Linear two-level programming deals with optimization problems in which the constraint region is implicity determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the linear two-level programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques. A small example is solved in order to illustrate the approach.