Sequential competitions with a middle-mover advantage

Highlights

• I model a sequential competition with perfect information and symmetric payoffs.

• The limiting logit equilibrium is used to refine the equilibria.

• The equilibrium predicts that the first- and last-movers earn the lowest payoffs.

• The equilibrium predicts that the middle-mover earns the highest (maximal) payoff.

• A lab experiment shows a middle-mover advantage and a first-/last-mover disadvantage.

Abstract

This paper investigates the incentives that drive advantageous positions in sequential competitions. Sequential competitions have been shown to have either a first- or last-mover advantage. In contrast, this paper illustrates a general sequential-move competition where the first- and last-moving agents are the least profitable while the middle-moving agent is guaranteed to earn the highest possible payoff. This result provide for a new intuition about the underlying incentives in a sequential decision structure which are tested using a multiple-round laboratory experiment. Experimental data aggregated across all rounds support the prediction of a first- and last-mover disadvantage along with a middle-mover advantage. Furthermore, the data suggest that subjects learn as they gain experience with this competition. In this manner, a sequential decision structure with inexperienced agents will benefit the first- and middle-moving agents, whereas the same decision structure with experienced agents will only benefit the middle-moving agents.

Introduction

This paper studies an environment where competitors make publicly observable choices according to an exogenously determined sequence. Previous research suggests that sequential competitions will endow an advantage to certain positions in the decision sequence. In most sequential settings, the advantageous position is either the first-mover or the last-mover.¹ The intuition behind these results is relatively straightforward. In some settings, first-movers can capitalize on a scarce resource, capture a desirable location, narrow down the competition, or develop a patented product, whereas in other scenarios, last-movers can learn about unknown market conditions or free-ride off of previous investments. However, a natural question is whether all sequential competitions can be classified as fair (where no inherent advantageous position exists), first-mover advantageous, or last-mover advantageous.

The main objective of this paper is to demonstrate a sequential competition which exhibits both a first- and last-mover disadvantage. In this manner, Sections 3 and 4 produce theoretical and experimental results which suggest a “middle-mover” advantage. The model presents an exogenously determined sequential competition where agents choose perfectly observable actions with the motivation of maximizing their symmetric and publicly-known payoff function (section 3.1). The Limiting Logit Equilibrium (McKelvey & Palfrey, 1995) of this highly symmetric model predicts that agents will earn different payoffs based solely on their position in the decision sequence (Results 1 and 2). In contrast with the previous literature, this paper’s equilibrium predicts that first- and last-movers will earn the lowest expected payoffs (first- and last-mover disadvantage), while the middle-mover is predicted to earn the maximum possible payoff (middle-mover advantage). Intuitively, the equilibrium suggests that every agent’s choice is influenced by two combating incentives. The “upstream” and “downstream” incentives encourage agents to make choices that adversely affect early-moving and late-moving agents, respectively (section 3.4). Section 4.1 describes a laboratory experiment used to test the prediction of a middle-mover advantage. Subjects interact in a sequential voting competition for 20 rounds where, in each round, subjects are randomly assigned a new group and a new position in the decision sequence. Section 4.2 discusses the experiment’s main findings which can be summarized with two points. First, the data support the model’s prediction of a middle-mover advantage along with a first- and last-mover disadvantage. Second, the repeated context of the experiment unearths a relationship between a subject’s experience with the competition and that subject’s responsiveness to the two combating incentives. Inexperienced subjects respond primarily to the downstream incentive whereas experienced subjects are more equally responsive to both the upstream and downstream incentives. The relationship between experience and behavior refines the expected outcome in this type of sequential competition. More specifically, a sequential competition with inexperienced agents greatly disadvantages the last-movers whereas the same competition with experienced agents is disadvantageous to both the first- and last-movers. Section 4.4 summarizes all of the experimental results.