Preemption Game Research Articles

Strategic investment under uncertainty: why multi-option firms lose the preemption run

We consider a dynamic duopoly game where firms choose both the timing and size of their investments. The existing real options literature predominantly consists of contributions where firms have a single option to invest. This paper relaxes this assumption by giving Firm A multiple options to undertake further investments with the purpose to expand whereas Firm B only holds the option to enter the market. In this asymmetric setting we get the surprising result that, in equilibrium, Firm B invests first. If Firm A invests first, Firm A and Firm B keep on being involved in preemption games for subsequent investments until Firm B enters the market, which leads to inefficiently early investments of Firm A. When Firm B invests first, then only one preemption game is played, which leads to Firm A being free to choose its unrestricted optimal investment moments.

The bidding strategy for renewable energy auctions under government subsidies

Investing in renewable energy is the inevitable path to achieving energy transition. To promote renewable energy investment, many countries have subsidized renewable energy generation alongside auction mechanisms. The bidding strategy for renewable energy auctions under different forms of government subsidies is not well studied. Based on the constructed preemption game model, this paper studies the bidding strategy for renewable energy auctions under government subsidies and further discusses the impact of different subsidy forms on the investor's bidding strategy. Our results demonstrate that with incomplete information on competitors' investment income or investment cost, an investor can refer to the bidding strategy without competitors to guide decisions. In addition, the higher the government subsidy, the lower the bidding price of the investor. In the fixed amount subsidy form, the most critical factor influencing the bidding strategy is the annual power production after the project investment.

Pioneer, early follower or late entrant: Entry dynamics with learning and market competition

Timing of market entry is one of the most important strategic decisions a firm must make, but its decision process becomes convoluted with information and payoff externalities. The threat of competition pushes firms to enter earlier to preempt their rivals while the possibility of learning makes them cautiously wait for others to take action. This combination amounts to a new class of timing games where a first-mover advantage first emerges as in preemption games but a second-mover advantage later prevails as in wars of attrition. Our model identifies under what conditions a firm becomes a pioneer, early follower or late entrant and provides efficiency implications by highlighting an elusive link between static market competition and dynamic entry competition.

The price-bidding strategy for investors in a renewable auction: An option games–based study

This paper presents a preemption game model based on real option theory to analyze the optimal bidding price for investors participating in a renewable auction. We studied how investors each decides their own optimal bidding price, with preemption by rivals and incomplete information, to balance their expected profits and ability to hedge risk. We demonstrate that adjusting the bidding price to hedge the risks from adverse market conditions can equal that of choosing a flexible investment time based on the standard real option model. The unique Bayesian Nash equilibrium of the game constituted with the optimal bidding price of each investor is also characterized. The quantitative solution to the model is provided, with integration of least squares Monte Carlo, and in the case study we calculate the optimal bidding price of offshore wind power concessions in China. An interesting finding in the quantitative evidence is that, although the optimal bidding price is close to zero net present value if the number of participants is large, with consideration of risk-hedging ability, investors may tend to play a hostile bid, which shows that a large number of participants may do harm to some renewable projects that are not mature enough.

Pioneer, Early Follower or Late Entrant: Entry Dynamics with Learning and Market Competition

Timing of market entry is one of the most important strategic decisions a firm must make, but its decision process becomes convoluted with information and payoff spillovers. The threat of competition pushes firms to enter earlier to preempt their rivals while the possibility of learning make them cautiously wait for others to take action. This combination amounts to a new class of timing games where first-mover advantage first emerges as in preemption games but second-mover advantage later prevails as in wars of attrition. Our model identifies under what conditions a firm becomes a pioneer, early follower or late entrant and shows that the timing of entry is excessively early (late) when there emerges a late entrant (early follower). We also argue that consumer inertia is often efficiency-enhancing in this environment, highlighting an elusive link between static market competition and dynamic entry competition.

Preemption contests between groups

AbstractWe consider a preemption game between competing groups; firms lobbying individually for their groups' interests provide an empirical example. Among symmetric groups, the first firm to take action bears an (unobserved) cost and wins the prize on behalf of its group. In equilibrium, the firm with the lowest cost takes action, but with delay. More competition and a smaller ratio of costs to benefits reduce delay. Firms in larger groups wait longer, but group action can occur earlier, as the probability of a low‐cost firm is higher. Asymmetries in group size or strength of externalities also matter.

Preemption Contests Between Groups

We consider a preemption game between groups where the first agent to take a costly action wins the prize on behalf of his group. We describe the equilibrium solution of this problem when players differ in their own costs of action and these costs are private information. The equilibrium is typically characterized by delay. The nature of the equilibrium depends on key parameters such as the number of groups and their size. More competition between groups reduces delay, whereas in larger groups members of a given cost type are more reluctant to act but may yield an earlier resolution of the conflict. We analyze asymmetries across groups, focusing on group size and strength of the externalities within groups.

A duopoly preemption game with two alternative stochastic investment choices

This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover.

Timing of entry and location/product differentiation

This research considers two alternative timing games, the precommitment game and the preemption game, where duopoly firms choose their respective timing of market entry and post‐entry profits are generated by price competition in a spatial model à la Hotelling (). We find that the time of first entry is increasing and the time of second entry is decreasing in location differentiation. The results are robust and valid both from an equilibrium analysis and from a welfare analysis. We also note that the difference in equilibrium entry times is too close from the viewpoint of social welfare.

Timing of entry and product location in a linear barbell model: Application to flexible manufacturing systems

This paper investigates a preemption game of entry into a market with endogenous product location so as to analyze the flexible manufacturing system. Based on a barbell model with continuous time and repeated purchases, we find that duopoly firms sequentially enter the market and differentiate maximally on product differentiation in equilibrium. The equilibrium timing differentiation between two firms is minimized among all product location combinations of them. We also conduct welfare analysis and show that the optimal differentiation in product location is similar to the equilibrium one, but there is market failure in the choice of entry timing. First entry occurs too late and second entry occurs too early (late, respectively) for a relatively more (less, respectively) flexible production system from the viewpoint of social welfare.

Subgame-perfect equilibria in stochastic timing games

We develop a notion of subgames and the related notion of subgame-perfect equilibrium – possibly in mixed strategies – for stochastic timing games. To capture all situations that can arise in continuous-time models, it is necessary to consider stopping times as the starting dates of subgames. We generalize Fudenberg and Tirole’s (Rev. Econom. Stud. 52, 383–401, 1985) mixed-strategy extensions to make them applicable to stochastic timing games and thereby provide a sound basis for subgame-perfect equilibria of preemption games. Sufficient conditions for equilibrium existence are presented, and examples illustrate their application as well as the fact that intuitive arguments can break down in the presence of stochastic processes with jumps.

Rushes in Large Timing Games

We develop a continuum player timing game that subsumes standard wars of attrition and pre-emption games, and introduces a new rushes phenomenon. Payoffs are continuous and single-peaked functions of the stopping time and stopping quantile. We show that if payoffs are hump-shaped in the quantile, then a sudden “rush” of players stops in any Nash or subgame perfect equilibrium. Fear relaxes the first mover advantage in pre-emption games, asking that the least quantile beat the average; greed relaxes the last mover advantage in wars of attrition, asking just that the last quantile payoff exceed the average. With greed, play is inefficiently late: an accelerating war of attrition starting at optimal time, followed by a rush. With fear, play is inefficiently early: a slowing pre-emption game, ending at the optimal time, preceded by a rush. The theory predicts the length, duration, and intensity of stopping, and the size and timing of rushes, and offers insights for many common timing games.

Strategic Technology Switching Under Risk Aversion and Uncertainty

Sequential investment opportunities or the presence of a rival typically hasten investment under risk neutrality. By contrast, greater price uncertainty or risk aversion increase the incentive to postpone investment in the absence of competition. We analyse how price and technological uncertainty, reflected in the random arrival of innovations, interact with attitudes towards risk to impact both the optimal technology adoption strategy and the optimal investment policy within each strategy, under a proprietary and a non-proprietary duopoly. Results indicate that technological uncertainty increases the follower's investment incentive and delays the entry of the non-proprietary leader, yet it does not affect the proprietary leader's optimal investment policy. Additionally, we show that technological uncertainty decreases the relative loss in the value of the leader due to the follower's entry, while the corresponding impact of risk aversion is ambiguous. Interestingly, we also find that a higher first-mover advantage with respect to a new technology does not affect the leader's entry, and that technological uncertainty may turn a pre-emption game into a war of attrition, where the second-mover gets the higher payoff.

Vertical governance change and product differentiation under decreasing component costs

In deciding on whether and when to outsource component production, firms should consider the trade-off between total production costs and the ability to horizontally differentiate products. We study the outsourcing decision in a duopoly under decreasing but uncertain market rates for components, given that outsourcing increases the substitutability of the final products. We find that there is at least one firm that eventually outsources component production because it cannot differentiate its product enough by in-house production to justify the (eventually) higher costs. The follower outsources at a lower market rate or may even remain vertically integrated. The follower thus incurs the (eventually) much higher in-house component costs longer, while the low substitutability is enjoyed by both firms. Under endogenous roles, firms thus engage in a preemption game to be the first to outsource. We also find that firms generally outsource at lower market rates if uncertainty is higher, but seek to preempt at remarkably higher market rates if substitutability remains low.

Preemption games under Lévy uncertainty

We study a stochastic version of Fudenberg–Tirole's preemption game. Two firms contemplate entering a new market with stochastic demand. Firms differ in sunk costs of entry. If the demand process has no upward jumps, the low cost firm enters first, and the high cost firm follows. If leader's optimization problem has an interior solution, the leader enters at the optimal threshold of a monopolist; otherwise, the leader enters earlier than the monopolist. If the demand admits positive jumps, then the optimal entry threshold of the leader can be lower than the monopolist's threshold even if the solution is interior; simultaneous entry can happen either as an equilibrium or a coordination failure; the high cost firm can become the leader. We characterize subgame perfect equilibrium strategies in terms of stopping times and value functions. Analytical expressions for the value functions and thresholds that define stopping times are derived.

Heterogeneity and Stability: Bolster the Strong, Not the Weak

We first study a stylized model of self-fulfilling panic among agents with differing fragilities to strategic risk and show that depending on the severity of coordination problems, the panic trigger threshold can depend only on one type's fragility. We then present a model of systemic panic among financial institutions with heterogeneous fragilities to financial spillovers. Concerns about potential spillovers generate strategic interaction, triggering a pre-emption game in which one tries to exit the market before others to avoid spillovers. Although financial contagion originates in weaker institutions, systemic risk can critically depend on financial health of stronger in the contagion chain. In this case, bolstering the strong, rather than the weak, more effectively enhances systemic stability.

CLUSTERING INN-PLAYER PREEMPTION GAMES

We study a complete information preemption game in continuous time. A finite number of firms decide when to make an irreversible, observable investment. Upon investment, a firm receives flow profits, which decrease in the number of firms that have invested. The cost of investment declines over time exogenously. We characterize the subgame-perfect equilibrium outcome, which is unique up to a permutation of players. When the preemption race among late investors is sufficiently intense, the preemption incentive for earlier investors disappears, and two or more investments occur at the same time. We identify a sufficient condition in terms of model parameters: clustering of investments occurs if the flow profits from consecutive investments are sufficiently close. This shows how clustering can occur in the absence of coordination failures, informational spillovers, or positive payoff externalities.

Heterogeneity and Stability: Bolster the Strong Not the Weak

This paper provides a model of systemic panic among financial institutions with heterogeneous fragilities. Concerns about potential spillovers from each other generate strategic interaction among institutions, triggering a preemption game in which one tries to exit the market before the others to avoid spillovers. Although financial contagion originates in weaker institutions, systemic risk depends critically on the financial health of stronger institutions in the contagion chain. This analysis suggests that when concerns about spillovers prevail, then 1) increasing heterogeneity of institutions promotes systemic stability and 2) bolstering the strong institutions in the contagion chain, rather than the weak, more effectively enhances systemic stability.

Competition, timing of entry and welfare in a preemption game

We show that in a preemption game of entry into a Cournot market, increasing the number of competitors beyond duopoly does not bring forward the time of first entry. We also show that all entries, except the first one, occur earlier than socially optimal.

Greed, Fear, and Rushes

We develop a simple new timing game that offers a unified theor y of sudden mass movements in economics, such as arise in matching, asset bubbles, and bank runs. We distinguish between rushes precipitated by greed and fear — i.e., the hunger for greater rewards from outlasting others, and the fear of missing out on early rewards. In our continuum player game, a payoff-relevant fundamental first “ripens”, peaks at a “harvest time”, and then “rots”. Payoffs are also scaled by a single-peaked quantile rank reward. Three local timing games arise in equilibrium: a war of attrition, a slow pre-emption game, and a pre-emptive rush. Our theory explains why matching rushes and bank runs happen inefficiently early, and asset sales rushes occur lat e. For with greed, the harvest time precedes an accelerating war of attrition ending in a rush, whereas with fear, an inefficiently early rush precedes a slowing pre-emption game ending at the harvest time. The theory yields consistent predictions for rush size, timing, gradual play timing, duration, and stopping rates. By our theory: (a) asset sales rushes reflect liquidity and relative compensat ion; (b) “unraveling” in matching markets depends on early matching stigma and market thinness; (c) illiquid bank loans yields complete bank runs before incomplete ones.