Abstract. This monograph examines monotone games and studies incentives and outcomes when there are multiple players, and how the decision of each player affects the well-being of others in particular ways. Games with strategic complements exhibit codirectional incentives, or incentives for each player to move in the same direction as other players. Games with strategic substitutes exhibit contradirectional incentives, or incentives for each player to move in the direction opposite to other players. Monotone games include both types of players: some players have incentives to move in the same direction as other players and some players have incentives to move in the direction opposite to other players.

This book develops the theory of monotone games in a new and unified manner and presents many applications. Incentives and outcomes studied in monotone games occur in a variety of disciplines, including biology, business, computer science, economics, mathematics, medicine, philosophy, political science, and psychology, among others. The book identifies unifying threads across different cases, showing how newer results are similar to or different from previous results, and how readers may better understand them under the umbrella of monotone games.

Abstract. Strategic complements are well understood for normal form games, but less so for extensive form games. There is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004)). We study necessary and sufficient conditions for strategic complements (defined as increasing best responses) in two stage, 2x2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. Payoffs with these conditions require the player to be indifferent between their actions in two of the four subgames in stage two, eliminating any strategic role for their actions in these two subgames. In contrast, the set of games that exhibit strategic complements (increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2x2 games (and provides a basis for possibly greater scope in more general games). The set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. The results are easy to apply, and are robust to including dual payoff conditions and adding a third player. Examples with several motivations are included.

Abstract: We investigate the accuracy of UPP as a tool in antitrust analysis when there are cost efficiencies from a horizontal merger. We include merger-specific cost efficiencies in a tractable manner in the model and extend the standard UPP formulation to account for these efficiencies. The efficacy of the new UPP formulations is analyzed using Monte Carlo simulation of 40,000 mergers (8 scenarios, 5,000 mergers in each scenario). We find that the new UPP formulations yield substantial gains in prediction of post-merger prices, and there are substantial gains in merger screening accuracy as well. Moreover, the new UPP formulations outperform the standard UPP formulation at higher thresholds for all the standard cases in the paper. The results are robust to several additional analyses. The results show that including cost efficiencies in a manner guided by the theoretical model may yield substantial improvements in accuracy of UPP as a tool in antitrust analysis.

Abstract: We extend the global games method to the class of finite player, finite action games that includes games with strategic complements, games with strategic substitutes, and arbitrary combinations of the two. Our result is based on common order properties present in both strategic complements and substitutes, the notion of p-dominance, and the use of dominance solvability as the solution concept. In addition to being closer to the original arguments in Carlsson and van Damme (1993), our approach requires fewer additional assumptions. In particular, we require only one dominance region, and no assumptions on state monotonicity, or aggregative structure, or overlapping dominance regions. As expected, the p-dominance condition becomes more restrictive as the number of players increases. In cases where the probabilistic burden in belief formation may be reduced, the p-dominance condition may be relaxed as well. We present examples that are not covered by existing results.

Abstract: We consider global games with general payoff structures and prove existence of equilibrium. This shows that the global games’ method is well defined with arbitrary strategic interaction among players, thus providing a foundation for the study of more general equilibrium behavior, especially as research in global games moves beyond the case of strategic complements. We also show that, in every global game, even though the information of each player is correlated, the joint information measure is absolutely continuous with respect to the product of its marginals. As one application, the result here can be used to show the existence of equilibrium in global games with both complementarity and congestion. This proves existence of equilibrium in a finite-player version of the model in Karp et al. (Games Econ Behav 60:155–175, 2007), thus addressing a gap in the proof of equilibrium existence documented in Hoffmann and Sabarwal (Games Econ Behav 94:188–190, 2015).

Abstract: Many questions of interest in economics can be stated in terms of monotone comparative statics: If a parameter of a constrained optimization problem increases, when does its solution increase as well. We characterize monotone comparative statics in different directions in finite-dimensional Euclidean space by extending the monotonicity theorem of Milgrom and Shannon (Econometrica 62(1):157–180, 1994) to constraint sets ordered in Quah (Econometrica 75(2):401–431, 2007)’s set order. Our characterizations are ordinal and retain the same flavor as their counterparts in the standard theory, showing new connections to the standard theory and presenting new results. The results are highlighted with several applications (in consumer theory, producer theory, and game theory) which were previously outside the scope of the standard theory of monotone comparative statics.

Abstract: This paper studies games with both strategic substitutes and strategic complements, and more generally, games with strategic heterogeneity (GSH). Such games may behave differently from either games with strategic complements or games with strategic substitutes. Under mild assumptions (on one or two players only), the equilibrium set in a GSH is totally unordered (no two equilibria are comparable in the standard product order). Moreover, under mild assumptions (on one player only), parameterized GSH do not allow decreasing equilibrium selections. In general, this cannot be strengthened to conclude increasing selections. Monotone comparative statics results are presented for games in which some players exhibit strategic substitutes and others exhibit strategic complements. For two-player games with linearly ordered strategy spaces, there is a characterization. More generally, there are sufficient conditions. The conditions apply only to players exhibiting strategic substitutes; no additional conditions are needed for players with strategic complements. Several examples highlight the results.

Abstract: In Karp et al. (2007), an argument is made to show existence of Bayesian–Nash equilibrium in global games that may include both strategic substitutes and complements. This note documents a gap in the proof of that statement.

Abstract: A partial test for strategic behavior in bankruptcy filing may be formulated by testing whether consumers manipulate their debt and filing decision jointly, or not: that is, testing for endogeneity of financial benefit and the bankruptcy filing decision. Using joint maximum likelihood estimation of an extended discrete choice model, test results are consistent with nonstrategic filing: financial benefit is exogenous to the filing decision. This result is confirmed in two different datasets (Panel Study of Income Dynamics and Survey of Consumer Finances). This result is consistent with an ex ante low net gain from a bankruptcy filing; a type of “rational inattention” to rare events such as bankruptcy.

Abstract: In games with strategic substitutes (GSS), convergence of the best-response dynamic starting from the inf (or sup) of the strategy space is equivalent to global stability (convergence of every adaptive dynamic to the same pure strategy Nash equilibrium). Consequently, in GSS, global stability can be analyzed using a single best response dynamic. Moreover, in GSS, global stability is equivalent to dominance solvability, showing that in this class of games, two different foundations for robustness of predicted outcomes are equivalent, and both can be checked using a single best response dynamic. These equivalences are useful to study stability of equilibria in a variety of applications. Furthermore, in parameterized GSS, under natural conditions, dynamically stable equilibrium selections can be viewed in terms of monotone selections of equilibria. Several examples are provided.

Abstract: Under some conditions, parameterized games with strategic substitutes exhibit monotone comparative statics of equilibria. These conditions relate to a tradeoff between a direct parameter effect and an opposing, indirect strategic substitute effect. If the indirect effect does not dominate the direct effect, monotone comparative statics of equilibria are guaranteed. These conditions are available for best-response functions, differentiable payoff functions, and general payoff functions. Results are extended to correspondences, the analysis applies to asymmetric equilibria, and several examples are provided.

Abstract: Securitization creates value for organizations, investors, and consumers:

  • It separates the funding of receivables from their origination and servicing, and allows origination and servicing revenues to grow without additional balance sheet financing.

  • It provides cash flow and balance sheet management benefits.

  • It allows for targeted asset liquidation, improvements in asset liquidity, and access to capital markets at rates different from enterprise credit ratings.

  • The flexibility in transforming risks permits mutually beneficial matches in targeted market opportunities, both for organizations and investors.

  • Deeper capital markets allow for price discovery of illiquid assets, greater access to funds for new firms and consumers, and greater financial innovation.

Securitization creates risks of moral hazard and lack of transparency;

  • Separation of funding from origination can create moral hazard, generating higher-than-expected risks and leading to conflicts between investors, firm shareholders, and firm creditors.

  • Complexity of structural transformations creates lack of transparency, which, in turn, can lead to greater illiquidity and possible market failure. These effects are worse in globally inter-connected markets.

Abstract: This paper presents a difference in the comparative statics of general equilibrium models with land when there are finitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb–Douglas utility, it is shown that with finitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by the consumer located at each fixed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each fixed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.

Abstract: This paper studies models where the optimal response functions under consideration are not increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be strategic complements. The main result here is that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Therefore, with multiple equilibria, some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium, or that use the lattice structure of the equilibrium set do not apply to such models. Moreover, there are no ranked equilibria in such models. Additionally, the analysis here implies a new proof and a slight generalization of some existing results. It is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)

Abstract: One explanation provided for the relatively high and increasingly stable spreads for moderate-sized IPOs ($20–$80 million) documented in Chen and Ritter (J Finance 55:1105–1131, 2000) is that issuing firms focus less on price and more on a combination of investment bank-differentiating factors (such as underwriter prestige, analyst coverage, industry expertise, under-pricing, price stabilization activities, liquidity provision, and so on), and banks use industry-based differentiation as a source of market power. Using a new approach developed in a model of firm location choice due to Ellison and Glaeser (J Politi Econ 105:889–927, 1997), this paper presents some evidence on the combined relevance of such bank-differentiating factors, over and above bank size, for firms choosing investment banks for floating IPOs. For moderate-sized IPOs, there is a little, but not much evidence that such factors are a good explanation for high and increasingly stable spreads. Other than in a few of the largest industries, bank-differentiating factors are not significantly relevant for a large proportion of industries. Moreover, one aggregate measure of differentiation is declining over time.

Abstract: In competitive economies with private firm ownership, incomplete markets, and firm shareholders changing over time, several firm objectives have been proposed. Some are useful to understand efficiency of equilibria, and others are explicitly consistent with majority shareholder control or collective choice rules, but it is not always clear if versions of each type are consistent with versions of the other type. This paper shows that ex-post, value maximizing rules, (including those proposed by Dreze, and Grossman and Hart,) are consistent with shareholder preferences in such economies; that is, along the equilibrium path, in every period and state of the world, every coalition of a firm’s shareholders in that period and state approves a value maximizing production plan. This result applies to cases when shareholders within a firm and across firms can form coalitions, and when stock trading can be ex-dividend or cum-dividend, and with a combination of both. This result does not resolve the problem of inefficiency of stock market equilibria, or that of ex ante disagreement among shareholders. It can help understand when firm objectives with some desirable properties are consistent with a particular version of shareholder control, and it provides a stability criterion (in terms of robustness to shareholder coalitions) for organizing productive resources in such economies.

Abstract: In recent years, one area of growing concern in corporate governance is the accounting and transfer of risk using special purpose entities (or trusts). Such entities are used widely in issuing asset-backed securities. This paper provides an overview of the asset-backed securities market, and discusses the common structures used in this market to transform the risks associated with the underlying collateral into risks associated with the issued securities. Understanding these structures is essential to understanding the allocation and transfer of risk among the different parties in an asset-backed transaction – the originator, the special-purpose entity, investors, and related parties such as insurance guarantors. Understanding these structures is also essential in proposing potential solutions to regulatory and accounting concerns about the transfer of risks in asset-backed securities.

Abstract: Limited liability debt financing of irreversible investments can affect investment timing through an entrepreneur’s option value, even after compensating a lender for expected default losses. This non-neutrality of debt arises from an entrepreneur’s unique investment opportunity, and it is shown in a standard model of irreversible investment that includes the equilibrium effect of a competitive lending sector. The analysis is partial, in that it takes as exogenously given an entrepreneur’s use of debt. Intuitively, limited liability lowers downside risk for the entrepreneur by truncating the lower tail of risks, and lowers the investment threshold. Compensating the lender for expected default losses reduces project profitability to the entrepreneur, and increases the investment threshold. The net effect is negative, because lower downside risk has an additional impact on the option value of delaying investment. The standard NPV rule in real options theory implicitly assumes debt to be neutral. With non-neutrality of debt, an investment threshold is higher than investment cost, but lower than the standard NPV rule. Comparisons with other standard investment thresholds show similar relationships.

Abstract: This paper uses novel data on the performance of loan pools underlying asset-backed securities to estimate a competing risks model of default and prepayment on subprime automobile loans. We find that prepayment rates increase rapidly with loan age but are not affected by prevailing market interest rates. Default rates are much more sensitive to aggregate shocks than are prepayment rates. Increases in unemployment precede increases in default rates, suggesting that defaults on subprime automobile loans are driven largely by shocks to household liquidity. There are significant differences in the default and prepayment rates faced by different subprime lenders. Those lenders that charge the highest interest rates experience the highest default rates, but also experience somewhat lower prepayment rates. We conjecture that there is substantial heterogeneity among subprime borrowers, and that different lenders target different segments of the subprime market. Because of their higher default rates, loans that carry the highest interest rates do not appear to yield the highest expected returns.

Abstract: Some results in the monotone comparative statics literature tell us that if a parameter increases, some old equilibria are smaller than some new equilibria. We give a sufficient condition such that at a new parameter value every old equilibrium is smaller than every new equilibrium. We also adapt a standard algorithm to compute a minimal such newer parameter value and apply this algorithm to a game of network externalities. Our results are independent of a theory of equilibrium selection and are valid for games of strategic complementarities.

Abstract: This paper constructs a model of an exchange economy in which bankruptcy arises in a manner similar to what we observe. Compared to related models, this model is a more realistic representation of some markets in which intertemporal assets are traded. Using standard and natural assumptions, it is shown that every economy represented by this model has an equilibrium. Therefore, bankruptcy can co−exist with smoothly functioning competitive markets in fairly general economies. Examples highlight some welfare effects of bankruptcy.