RESEARCH
We investigate agents' incentives to form mergers (or groups) by sharing their private information and the associated welfare effects in aggregative games. The merging agents always have incentives to share their information with each other in horizontal/conglomerate merger games. A merger decreases the expected payoff of each merging agent if and only if the strategies of agents are sufficiently high strategic substitutes and the number of merging agents is sufficiently low under complete or too noisy information. Expected consumer and total welfare may increase after a horizontal/conglomerate merger or common/cross ownership with information efficiencies in Cournot and Bertrand games with substitutable or complementary products. Moreover, a group of any size increases (decreases) expected total efforts in partnership games with complementary (substitutable) strategies; it increases public good contributions, gas emission abatements, and decreases expected total resource extractions in public good provision, gas emission, and common-resource games, respectively; and it increases expected welfare in these games. Finally, we study the value and aggregation of information in our set-up.
This study pursues how waitlists should be designed to achieve desirable outcomes in canonical object allocation models. We adapt the usual stability notion to our setting and call it “sure stability.” Our first mechanism—Deferred Acceptance with Straightforward Waitlists (DSW)—is surely stable. However, sure stability is incompatible with strategy-proofness, implying that DSW is vulnerable to preference misreportings. Our second mechanism—Serial Dictatorship with Straightforward Waitlists (SSW)—is surely strategy-proof, a stronger version of strategy-proofness. Whenever waitlist capacities are unlimited, DSW is the essentially unique constrained efficient mechanism, and SSW is efficient. They, however, lose these efficiency properties under limited waitlists. Our last mechanism—Deferred Acceptance with Augmented Waitlists (DAW)—is surely stable and improves DSW whenever waitlist capacities are capped. We also show that under each of these mechanisms, increasing the waitlist capacities always at least weakly welfare-improving.
''Acquisition, Aggregation, and Sharing of Information in Sequential-move Aggregative Games", 14 April 2021, pdf, Online Appendix A pdf, Online Appendix B (Mathematica File): Computations.nb
We study quadratic payoff common-value aggregative games with signaling, where n privately informed agents choose actions sequentially. Applications include Stackelberg quantity-setting, public good contribution, common resource, and gas emission games. Whereas efficient aggregation of information occurs in large Stackelberg markets, it does not occur in the three remaining large markets. If all agents share their information only with their followers or with each other, expected welfare increases in the Stackelberg game and it decreases in the remaining three games. The first n-1 agents have incentives to share their information with their follower(s) if n = 2 or the signals' precision is sufficiently low. For n = 2, more imprecise own information benets an agent if and only if the precision of the follower's signal (τ2) is sufficiently low. Moreover, expected welfare decreases with the precision of the public signal in the Stackelberg game (the three remaining games) if τ2 is not suciently low or high (is suciently high). We provide robustness checks in private-value aggregative games and in quasi-aggregative games between one manufacturer and n-retailers.
''Stackelberg versus Cournot Oligopoly with Private Information", November 2020, pdf , Online Appendix B, pdf , Online Appendix C (Mathematica file): Computations.nb
We compare an n-firm Cournot model with a Stackelberg model, where n-firms choose outputs sequentially, in a stochastic demand environment with private information. The expected total output, consumer surplus, and total surplus are lower, while expected price and total profits are higher in the Stackelberg perfect revealing equilibrium (SPRE) than in the Cournot equilibrium. These rankings are the opposite to the rankings of prices, total output, surplus, and profits under perfect information. We also show that the first n-1 firms' expected profits form a decreasing sequence from the first to the (n-1)st in the Stackelberg game. The last mover earns more expected profit than the first mover if n<5 or the ratio of the signals' informativeness to the prior certainty is sufficiently low enough. Lastly, there is a discontinuity between the Stackelberg equilibrium of the perfect information game and the limit of Stackelberg perfect revealing equilibria, as the noise of the demand information of all firms vanishes to zero at the same rate. We provide various robustness checks for the results when the precision of signals are asymmetric, there is public information or cost/quality uncertainty, or the products are differentiated.
Supply/Demand Function Competition with Heterogeneously Correlated Errors and Signals, (with Carolina Manzano), 15 February 2018
Three assumptions in Vives (2010, 2011) are that traders (or firms) have homogenously correlated signals, errors are not correlated, and signals and their priors have normal distributions. In this paper, we first show that all results of Vives (2010, 2011), Rostek and Weretka (2012, 2015), and Ollar (2017) are robust in a richer set-up, where i) traders (or firms) have heterogeneously correlated signals and ii) prior-signal distribution pairs satisfy beta-binomial, gamma-poisson, and normal-normal distributions. Moreover, Propositions 1 and 2 of Rostek and Weretka (2012) follow from Proposition 1 of Vives (2010) after we let the aggregated quantity supplied of the traded asset be zero. Lastly, the comparative statics of RW (2012, 2015) and Ollar (2017) regarding the non-monotonic effect of market size on the price informativeness hold in our generalized supply function model of Vives (2011) with normally distributed pairs. The main intuition behind the findings is that the equilibrium bids of traders (or firms) do not change as we move from the homogeneously correlated signals and errors model to the heterogonously correlated signals and errors model under the equicommonality assumption.
Multi-Product Assortment and Competition: Comment, (with Gabor Virag), First Version: 20 November 2017, This Version: 23 March 2018, pdf
Federgruen and Hu (FH) (2015-2017b) claim that there is a unique Bertrand equilibrium in the set-up of Cumbul and Virag (CV) (2017) with further restrictions of positive demand intercepts and substitutable products. This equilibrium is weakly dominated as all inactive firms (if they exist) charge below their marginal cost levels. However, CV (2017) show that there is a continuum of undominated equivalent or non-equivalent Bertrand equilibria when some firms are inactive. In this note, we explain why the Bertrand equilibrium characterization results of these papers contradict each other. We also point out some negative properties of the special equilibrium that is studied in FH (2015-2018). Our arguments provide support for why the undominated equilibria of CV (2017) can be chosen over the weakly dominated special equilibrium of FH (2015-2018) when some firms are inactive.
"Information Acquisition and Sharing with Asymmetric Supply/Demand Functions", (with Carolina Manzano), First Version: 15 November 2015, This Version: 15 February 2017
There has been an extensive debate about the enforcement of regulations to enhance wholesale electricity and financial market integrity and transparency in the EU and the US. In this paper, we study i) How such regulations affect market competitiveness and ii) The incentives of firms to acquire or share cost information. We consider two (potentially) asymmetrically and privately informed firms (traders resp.) facing linear stochastic costs (asset values) and engaging in supply (demand) function competition. We show that expected- consumer surplus (auctioneer surplus) and total welfare increase with both information- sharing and acquisition due to the increase in the overall competition level. More informed firms choose steeper supply (demand) functions and have more market power compared to less informed firms. Moreover, as firm i gets more informed, expected price (quantity of firm i) increases if and only if its rival's supply function slopes downwards (upwards) and the prior mean of its cost is sufficiently low. However, better information may also increase expected profit by raising production volatility. A firm has an incentive to acquire (observable) information if i) the rival firm is sufficiently informed or ii) both the correlation between firms' cost parameters (ρ) and the demand intercept are sufficiently low or iii) both ρ and the prior mean of its cost are low. With linear costs, full-sharing equilibrium does not exist. Nevertheless, a firm has an incentive to unilaterally share his information for free if ρ is sufficiently low or high for a large set of parameter values. Various extensions of the findings are provided when i) there are two groups of asymmetrically informed bidders; or ii) two bidders have heterogeneous transactions costs; or iii) information structure allows for noisy confounding; or iv) n bidders have asymmetrically correlated values.
"Multilateral Limit Pricing in Price-Setting Games", 18 April 2018, (with Gabor Virag), pdf , forthcoming in the Games and Economic Behavior
ABSTRACT: In this paper, we characterize the set of pure strategy undominated equilibria in differentiated Bertrand oligopolies with linear demand and constant unit costs when firms may prefer not to produce. When all firms are active, there is a unique equilibrium. However, there is a continuum of non-equivalent Bertrand equilibria on a wide range of parameter values when the number of firms (n) is more than two and n*∈ [2,n-1] firms are active. In each such equilibrium, the firms that are relatively more cost or quality efficient limit their prices to induce the exit of their rival(s). When n>2, this game do not need to satisfy supermodularity, the single-crossing property (SCP), or log-supermodularity (LS). Moreover, the best responses might have negative slopes. These results are very different from those in the existing literature on Bertrand models with differentiated products, where uniqueness, supermodularity, the SCP, and LS usually hold under a linear market demand assumption, and best response functions slope upward. Our main results extend to a Stackelberg entry game where some established incumbents first set their prices, and then a potential entrant sets its price.
''Third Degree Price Discrimination in Input Markets with Private Information'', 30 June 2016, pdf
In a world of perfect information, it is well-known that a manufacturer prefers to price discriminate between its retailers with different cost efficiencies rather than to offer a uniform price to them. Moreover, price discrimination creates allocative inefficiencies, hurts consumers, and decreases social welfare. In this paper, we investigate third degree price discrimination incentives of a manufacturer between its retailers and the associated welfare consequences of price discrimination in input markets with stochastic demand. We consider a channel structure where a manufacturer and two quantity competing retailers have private signals about demand and retailers face identical firm specific costs. Unlike perfect information, we show that a manufacturer would to like set a uniform wholesale (input) price rather than to charge different prices to its retailers. Moreover, consumers prefer price discrimination over uniform pricing. Lastly, social welfare is higher with price discrimination. The results provide theoretical background for why we observe price discrimination in some input markets while uniform pricing is adopted in others.
''The Welfare Effects of Mergers in Differentiated Product Markets'', 2013 pdf, mimeo
ABSTRACT: In this paper, we investigate the welfare effects of horizontal mergers on merging firms (insiders), non-merging firms (outsiders), and consumers in a differentiated product market. If mergers do not generate any cost efficiencies, then any size of mergers among firms producing substitutable goods always decreases both consumer- and total welfare under both quantity and price setting games. We also introduce a price approach for calculating total welfare to understand the specific effects causing these very negative results. Similarly, merger simulations in the heterogeneous costs model strongly suggest that mergers with full cost efficiency gains are still mostly welfare declining especially when marginal cost over demand ratio is low. However, if the goods are complements of each other, then mergers might be welfare enhancing under both models.
We also discuss that since the variety effect dominates the competition effect, both consumer surplus and total welfare decline in the degree of substitution. Lastly, we compare a k-firm Cournot merger with a k-firm Bertrand merger. Bertrand competition is more competitive than Cournot competition and results in higher both consumer- and total welfare for any number of firms merged.
''An Algorithmic Approach to Finding Nash Equilibria in Cournot and Bertrand Games with Potential Entrants'', 2013, mimeo
ABSTRACT: In this paper, we consider a market with potential entrants and incumbents. To describe entry and exit decisions of firms, we characterize the whole set of equilibria(um) in Cournot- and Bertrand models. We relax the assumption of positive outputs and provide some algorithms to find the firms which actively produce in these models. Our results show that there is a unique pure strategy Cournot-Nash equilibrium, where only the firms survived from an efficient iteration algorithm produce under two different models: 1-) High-degree heterogenous goods, linear demand, different constant costs 2-) Low-degree heterogeneous goods, declining marginal revenues, convex or not too concave costs. Additionally, we study Bertrand models and argue why an established firm can decrease its price in equilibrium when it is faced with a low threat potential entrant firm. Further, we charecterize the whole set of multiple undominated Bertrand-Nash equilibria. Moreover, Bertrand best replies might be negatively sloped (i.e, the game is not supermodular) on some part of the domain when the number of firms is more than two. These results are very different from the existing literature on Bertrand models, where uniqueness usually holds under a linear market demand assumption and best reply functions slope upwards. Finally, we apply these models to a merger-setting and show that exit-inducing Cournot and Bertrand horizontal mergers should be allowed from both a consumer welfare and total welfare point of view, which contradicts the conventional wisdom.