Entry Game Research Articles

Endogeneity in Discrete Bayesian Games: U.S. Cellphone Service Deployment

In some Bayesian games, payoff-relevant states are influenced by unobserved player- or game-level heterogeneity that also also effects strategic decisions directly. Ignoring such endogeneity in empirical analysis leads to erroneous inference of structural parameters and policy implications. We introduce a control-function approach for estimating discrete Bayesian games with such endogeneity. We apply the method to analyze an entry game of deploying 4G-LTE technology by major U.S. cellphone service providers, taking existing network deployment in the focal market and current deployment in neighboring markets as endogenous. Using lagged demographics of neighboring markets as instruments, we find that a hypothetical T-Mobile and Sprint merger would reduce 4G-LTE deployment across local markets. Moreover, the entry of a fourth national provider, enabled by a partial divestiture of the merger’s assets, would not completely offset its negative impact on market entries and the population served. We also find that ignoring endogeneity in network deployment skews the policy implications by underpredicting the merger’s negative impacts on market entry.

Superstar exporters: An empirical investigation of strategic interactions in Danish export markets

In many countries, exports are highly concentrated among a few “superstar” firms. We estimate the export decisions of superstar firms as the result of a complete information, simultaneous, discrete choice, static entry game. We employ a dataset on the universe of Danish trade transactions by firm, product and destination. We also obtain detailed information on applied, preferential tariff protection from the MAcMap-HS6 database. We find evidence of strong negative competitive effects of entry: in the absence of strategic competitive effects, firms would be 53.2 percentage points more likely to export to a given market. Next, we run two counterfactual exercises. We show that failing to account for the strategic interaction among superstar exporters leads to: (i) overstating the probability that firms would start exporting to a market following tariff elimination by a factor of two; and, (ii) overstating the probability that firms would stop exporting to a market if tariffs were imposed by a factor of more than five.

Superstar Exporters: An Empirical Investigation of Strategic Interactions in Danish Export Markets

In many countries, exports are highly concentrated among a few superstar' firms. We estimate the export decisions of superstar firms as the result of a complete information, simultaneous, discrete choice, static entry game. We employ a dataset on the universe of Danish trade transactions by firm, product and destination. We also obtain detailed information on applied, preferential tariff protection from the MAcMap-HS6 database. We find evidence of strong negative competitive effects of entry: in the absence of strategic competitive effects, firms would be 53.2 percentage points more likely to export to a given market. Next, we run two counterfactual exercises. We show that failing to account for the strategic interaction among superstar exporters leads to: \emph{(i)} overstating the probability that firms would start exporting to a market following tariff elimination by a factor of two; and, \emph{(ii)} overstating the probability that firms would stop exporting to a market if tariffs were imposed by a factor of more than five.

Limit Pricing and Entry Game of Renewable Energy Firms into the Energy Sector

Governments attempt to provide the energy sector with incentives to replace old technologies with new ones based on renewable energy as the most effective way to combat climate change. Yet, in the energy sector prevail fossil fuel incumbents that inhibit renewable energy entrants. Our paper provides a game-theoretic stylization of competition between those two types of firms. Incumbents set prices and entrants respond with quantity adjustments. In the context of a dynamic limit pricing model, we study the entry dynamics in a market in which the dominant firms (fossil fuel energy suppliers) face the entry of a group of competitive fringe firms (renewable energy suppliers) when the dominant firms have easier access to financial markets, but the fringe firms finance their expansion with internal finance. We also investigate the effect of the public support of renewable energy firms through subsidies. Our model is built on Judd and Peterson (1986, JET), but our solutions are obtained through a non-linear model predictive control algorithm. By this technique, we can predict the outcome of the competition between incumbents and entrants and the impact of financial and fiscal policies considering moving-horizon strategies.

Meaning and credibility of forward-looking disclosures: evidence from an entry game

Purpose- The study aims to find and analyze the equilibria for the forward-looking disclosures using game theory and to investigate the information signaling mechanism of such disclosures focusing on the credibility and meaning of them. Methodology- The study uses a cheap-talk game setting as a special form of signaling game in which forward-looking information are examined as costless, nonbinding and non-verifiable claims sent to a potential Entrant by the Incumbent firm. Findings- Equilibria are derived and neologism-proofness refinement is applied to rule out the implausible equilibria. Informative equilibrium exists only if the players’ preferences are more closely aligned. Entrant’s strategy is critical to determine which equilibrium is plausible. Under entry strategy, informative equilibrium is plausible and rules out the uncommunicative equilibria. However, under non-entry strategy, informative equilibrium fails to be plausible. Conclusion- Only under the entry strategy, the Incumbent should disclose its private information, whereas, under non-entry strategy, the Incumbent should not reveal its private information. Furthermore, the uncommunicative equilibria indicate that despite the Entrant’s pessimism about future, the Entrant prefers to choose entry strategy when the entry cost is sufficiently low. Contrarily, despite the Entrant’s optimism, non-entry becomes optimal when the entry cost is relatively high.

Estimation of the static corporate sustainability interactions

ABSTRACT The empirical literature considers firm-specific aspects affecting corporate sustainability decisions but generally omits the influence of the competition. We advocate that sustainability actions of a company impact its marketplace and vice versa. Therefore, the sustainability return of the single firm is a function of the other firms’ sustainability decisions. We approach sustainability decisions as strategic decisions and evaluate the effect of competition and spillovers in a static market entry game. We estimate the parameters of the discrete choice model using the social performance ratings from MSCI KLD 400 Social Index as proxy for sustainability decisions and financial information from Wharton Research Data Services’ COMPUSTAT dataset. When strategic interaction is not accounted for, we find that an increase in the number of competitors increases the likelihood of sustainability investments, seemingly shows the spillover effect dominates the competition. When we apply the multi-stage approach, which incorporates competitive interaction, we provide empirical evidence that the effect of competition on the likelihood of entry into the sustainability market dominates the effect of spillover. We find that strategic motives, typically ignored in the empirical literature, appear to be an important factor in understanding sustainability-related decisions.

Entry Timing in the Face of Switching Costs and its Welfare Effects: Evidence from Same-Day Grocery Delivery Platforms

The online grocery market has seen significant entry over the last five years by firms with different business models. Most firms offer subscriptions, and, in the data, consumers rarely switch between them. I find that switching costs significantly affect consumer platform choice, suggesting potential for future exercise of market power. I estimate the welfare impact of the acquisition of a national grocery chain by of a major online retailer and highlight the role played by this feature of demand and by delivery cost structures. I model competition between two large platforms. The first is the major online retailer engaging in the merger. The rival is an independent platform with low entry costs. The platforms compete in a dynamic entry game, and two opposing forces influence entry timing. I find that firms chase a first-mover advantage resulting from consumer lock-in at the expense of higher entry costs, leading to significant costs of early entry. I estimate that, before the acquisition, the major online retailer had very large entry costs. The acquisition reduced this cost, posing a competitive threat to the rival. Consumer lock-in then contributed to raising the stakes of early entry for both firms, accelerating entry across new markets and generating over \$ 800 M in welfare gains to consumers due to earlier entry. Further, I find that a merger between the two platforms, resulting in a monopoly, would delay entry significantly. These results show that strategic competition in entry timing plays an important role in mergers' welfare effect.

The differential impact of friendship on cooperative and competitive coordination

Friendship is commonly assumed to reduce strategic uncertainty and enhance tacit coordination. However, this assumption has never been tested across two opposite poles of coordination involving either strategic complementarity or substitutability. We had participants interact with friends or strangers in two classic coordination games: the stag-hunt game, which exhibits strategic complementarity and may foster “cooperation”, and the entry game, which exhibits strategic substitutability and may foster “competition”. Both games capture a frequent trade-off between a potentially high paying but uncertain option and a low paying but safe alternative. We find that, relative to strangers, friends are more likely to choose options involving uncertainty in stag-hunt games, but the opposite is true in entry games. Furthermore, in stag-hunt games, friends “tremble” less between options, coordinate better and earn more, but these advantages are largely decreased or lost in entry games. We further investigate how these effects are modulated by risk attitudes, friendship qualities, and interpersonal similarities.

A geometric approach to inference in set-identified entry games

In this paper, we consider inference procedures for entry games with complete information. Due to the presence of multiple equilibria, we know that such a model may be set-identified without imposing further restrictions. We complete the model with the unknown selection mechanism and characterize geometrically the set of predicted choice probabilities, in our case, a convex polytope with many facets. Testing whether a parameter belongs to the identified set is equivalent to testing whether the true choice probability vector belongs to this convex set. Using tools from the convex analysis, we calculate the support function and the extreme points. The calculation yields a finite number of inequalities, when the explanatory variables are discrete, and we characterized them once for all. We also propose a procedure that selects the moment inequalities without having to evaluate all of them. This procedure is computationally feasible for any number of players and is based on the geometry of the set. Furthermore, we exploit the specific structure of the test statistic used to test whether a point belongs to a convex set to propose the calculation of critical values that are computed once and independent of the value of the parameter tested, which drastically improves the calculation time. Simulations in a separate section suggest that our procedure performs well compared with existing methods.

Competition and mergers in the retail market for toys

ABSTRACT I study competition between big box retailers, K-Mart and Wal-Mart, and toy retailers, KB Toys and Toys R Us with the aim of estimating Wal-Mart’s effect on the profits of toy retailers. Using recent techniques for the moment inequality models, I estimate chains’ exit decisions in each market as arising from a Nash equilibrium of a static game of entry and exit. My results show that Wal-Mart has a significantly negative effect on the profits of KB Toys and Toys R Us, while the effects of KB Toys and Toys R Us are mostly positive on each other’s profits. I run a series of counterfactual simulations to study the effect of a merger between KB Toys and Toys R Us on post-merger market shares and concentration. Upon merging, the rate of exit drops from 52.3% to 48.6% for KB Toys and from 32.1% to 11.7% for Toys R Us. If the merging parties share distribution centres, the rate of exit drops even further to 31.1% for KB Toys or remains about the same at 12.2% for Toys R Us. Surprisingly, the merger lowers market concentration, as measured by the Herfindal–Hirschman Index.

Information Correlation in a 2 × 2 Game and an Extension of Purification Rationale

In this paper, we study a 2 × 2 Bayesian entry game with correlated private information. The distribution of private information is modelled by a symmetric joint normal distribution. Therefore, the correlation coefficient of the private information distribution reflects the degree of dependence of players' private information. Under such specification, players' private information can be correlated flexibly, which is not confined to the typical additive specification of private payoff shocks or private information by Carlson and van Damme (1993), where the private information is correlated due to the common payoff shock. In our game, if the private information is correlated, we find that given the variances of the private information, there exists a restriction on the degree of correlation of players' private information that allows the game can be solved by cutoff strategies. Specifically, given the variances of the private information, if players' private information in strategic substitutes (strategic complements) Bayesian games are positively (negatively) correlated, the range of correlation coefficient that allows the game can be solved by cutoff strategies is restricted so that if the correlation is out of the range, the game cannot be solved by cutoff strategies. Alternatively, given positive (negative) correlation of private information, the value of variances that allows a strategic substitutes (strategic complements) Bayesian games can be solved by cutoff strategies are restricted within certain range. If the value of variances fall out of the range, the Bayesian game cannot be solved by cutoff strategies. However, given negative (positive) correlation of players' private information in strategic substitutes (strategic complements) Bayesian games, in which the Bayesian games can always be solved by cutoff strategies, we prove that as the variances converge to zero, all pure strategy Bayesian Nash equilibria of the perturbed games converge to the respective Nash equilibria of the corresponding strategic substitutes (strategic complements) complete information games. Based on the result, we conclude that the purification rationale proposed by Harsanyi (1973) can be extended to games with dependent perturbation errors that follow a symmetric joint normal distribution if the correlation coefficient is positive for the strategic complements games or negative for the strategic substitutes games.

Investment in Green Technology and Entry Deterrence

Abstract This paper analyzes an entry-deterrence model in which the incumbent decides whether to invest in research and development (R&D) that promotes clean technology. We consider the case in which the entrant could benefit from a technology spillover and analyze the conditions that facilitate the incumbent’s entry-deterrence behavior. We show that higher levels of the spillover make entry more attractive compared to a standard entry game. In addition, regulator and incumbent prefer entry when the spillover from clean technology is sufficiently high and the cost of investing in R&D is relatively low. However, preferences are misaligned when the spillover and cost of R&D are low.

Testing for the emergence of spontaneous order

We report on an experimental investigation of the emergence of Spontaneous Order, the idea that societies can co-ordinate, without government intervention, on a form of society that is good for its citizens, as described by Adam Smith. Our experimental design is based on a production game with a convex input provision possibility frontier, where subjects have to choose a point on this frontier. We start with a simple society consisting of just two people, two inputs, one final good and in which the production process exhibits returns to specialisation. We then study more complex societies by increasing the size of the society (groups of 6 and 9 subjects) and the number of inputs (6 and 9 inputs respectively), as well as the combinations of inputs that each subject can provide. This form of production can be characterised as a cooperative game, where the Nash equilibrium predicts that the optimal outcome is achieved when each member of this society specialises in the provision of a single input. Based on this framework, we investigate whether Spontaneous Order can emerge, without it being imposed by the government. We find strong evidence in favour of the emergence of Spontaneous Order, with communication being an important factor. Using text classification algorithms (Multinomial Naive Bayes) we quantitatively analyse the available chat data and we provide insight into the kind of communication that fosters specialisation in the absence of external involvement. We note that, while communication has been shown to foster coordination in other contexts (for example, in public goods games, market entry games and competitive coordination games) this contribution is in the context of a production game where specialisation is crucial.

The Circular City with Heterogeneous Firms

The paper extends the Salop model of localized competition by allowing rms to have heterogeneous costs. We provide a general but highly tractable analytical solution for the equilibrium prices, and we study the long-run properties of the model using two dierent entry games. We show that cost heterogeneity aects the eciency of the market equilibrium by increasing welfare and inducing less excessive entry. Further, we illustrate the positive eects of the existence of a selection mechanism, which induces less ecient rms not to start production. The model also replicates some recent results on dense markets.

Enteroviruses: A Gut-Wrenching Game of Entry, Detection, and Evasion.

Enteroviruses are a major source of human disease, particularly in neonates and young children where infections can range from acute, self-limited febrile illness to meningitis, endocarditis, hepatitis, and acute flaccid myelitis. The enterovirus genus includes poliovirus, coxsackieviruses, echoviruses, enterovirus 71, and enterovirus D68. Enteroviruses primarily infect by the fecal–oral route and target the gastrointestinal epithelium early during their life cycles. In addition, spread via the respiratory tract is possible and some enteroviruses such as enterovirus D68 are preferentially spread via this route. Once internalized, enteroviruses are detected by intracellular proteins that recognize common viral features and trigger antiviral innate immune signaling. However, co-evolution of enteroviruses with humans has allowed them to develop strategies to evade detection or disrupt signaling. In this review, we will discuss how enteroviruses infect the gastrointestinal tract, the mechanisms by which cells detect enterovirus infections, and the strategies enteroviruses use to escape this detection.

Confidence Intervals for Projections of Partially Identified Parameters

We propose a bootstrap‐based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the function of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the function of θ, not θ itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Nonetheless, the program defining an extreme point of the confidence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately, and we establish its rate of convergence. The algorithm is of independent interest for optimization problems with simple objectives and complicated constraints. An empirical application estimating an entry game illustrates the usefulness of the method. Monte Carlo simulations confirm the accuracy of the solution algorithm, the good statistical as well as computational performance of calibrated projection (including in comparison to other methods), and the algorithm's potential to greatly accelerate computation of other confidence intervals.

Morphisms of Open Games

We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the (perhaps more intuitively obvious) definition of globular morphisms as mappings between strategy profiles that preserve best responses, and hence in particular preserve Nash equilibria. We construct a symmetric monoidal double category in which the horizontal 1-cells are open games, vertical 1-morphisms are lenses, and 2-cells are morphisms of open games. States (morphisms out of the monoidal unit game) in the vertical category give a flexible solution concept that includes both Nash and subgame perfect equilibria. Products in the vertical category give an external choice operator that is reminiscent of products in game semantics, and is useful in practical examples. We illustrate the above two features with a simple worked example from microeconomics, the market entry game.

An Entry Game with Learning and Market Competition

This paper provides a dynamic game of market entry to illustrate entry dynamics in an uncertain market environment. Our model features both private learning about the market condition and market competition, which give rise to the first-mover and second-mover advantages in a unified framework. We characterize symmetric Markov perfect equilibria and identify a necessary and sufficient condition for the first-mover advantage to dominate, which elucidates when and under what conditions a firm becomes a pioneer, an early follower or a late entrant. We also derive equilibrium payoff bounds to show that pioneering entry is generally payoff-enhancing, even though it is driven by preemption motives, and discuss efficiency properties of entry dynamics.

Candidate Entry and Political Polarization: An Experimental Study

We report the results of a laboratory experiment based on a citizen–candidate model with private information about ideal points. Inefficient political polarization is observed in all treatments; that is, citizens with extreme ideal points enter as candidates more often than moderate citizens. Second, less entry occurs, with even greater polarization, when voters have directional information about candidates’ ideal points, using ideological party labels. Nonetheless, this directional information is welfare enhancing because the inefficiency from greater polarization is outweighed by lower entry expenses and better voter information. Third, entry rates are decreasing in group size and the entry cost. These findings are all implied by properties of the unique symmetric Bayesian equilibrium cutpoint pair of the entry game. Quantitatively, we observe too little (too much) entry when the theoretical entry rates are high (low). This general pattern of observed biases in entry rates is implied by logit quantal response equilibrium.

License Complementarity and Package Bidding: The U.S. Spectrum Auctions

The U.S. spectrum licenses cover geographically distinct areas and are often complementary to each other. A bidder seeking to acquire multiple licenses is then exposed to risks of winning only isolated patches. To allocate licenses more efficiently, the Federal Communications Commission allowed bidders to bid for (predefined) packages of licenses in Auction 73. We estimate the magnitude of license complementarity by modeling the bidding process as an entry game with interdependent markets and evolving bidder belief. Bidders' decisions on bidding (and not bidding) provide bounds on licenses' stand-alone values and complementarity between licenses. We estimate the total complementarity to be around two thirds of the total bidding ($19 billion) in Auction 73. Complementarity in a 1 MHz nationwide license is worth $918 million to an average large bidder but only $120 million to an average small bidder. Our counterfactual analysis shows that the effects of package bidding on bidders' exposure risks depend on package format and package size. More importantly, mixed package bidding increases FCC revenue substantially at the cost of reducing bidder surplus and increasing license allocation concentration.