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We introduce a behavioral contract theory idea, “shading” (Hart and Moore (2008). “Contracts as Reference Points.” Quarterly Journal of Economics 123 (1): 1–48)) as a component of ex-post haggling (addressed by Coase (1937. “The Nature of the Firm.” Economica 4 (16): 386–405) and Williamson (1975. Markets and Hierarchies: Analysis and Antitrust Implications. New York: Free Press)) into the collusion model à la Tirole (1986. “Hierarchies and Bureaucracies: On the Role of Collusion in Organizations.” Journal of Law, Economics, and Organization 2 : 181–214, 1992. “Collusion and the Theory of Organizations.” In Advances in Economic Theory: The Sixth World Congress, edited by J. J. Laffont. Cambridge: Cambridge University Press), thereby constructing a new model of hierarchical organization. By integrating the two ideas, i.e. collusion and shading, we enrich the existing collusion model, thereby obtaining a new result for Collusion-proof versus Equilibrium Collusion. The basic idea is that the increase in shading pressure strengthens the incentive for collusion, thereby making it difficult to implement collusion-proof incentive schemes, which leads to the Equilibrium Collusion. In addition, we also provide a micro-foundation for ex-post haggling costs, where we view rent-seeking associated with collusive behavior and ex-post haggling generated from aggrievement and shading as the two sources of the costs. This model is used to examine the optimal organizational design problem as an optimal response to the trade-off between gross total surplus and ex-post haggling costs, and to take a step further the idea of efficient organization design (Milgrom (1988. “Employment Contracts, Influence Activities and Efficient Organization Design.” Journal of Political Economy 96 : 42–60)). We believe that our model could help provide a deep understanding of resource allocation and decision processes in hierarchical organizations.

Progress of hardware technologies and diffusion of computer knowledge enable consumers to crack software if they decide to use software illegally. This paper constructs a software market in which consumers are horizontally differentiated in accordance with social norms of copyright protection to examine the monopolistic producer’s software protection behaviors with considering partial compatibility between genuine and cracked software as well as utility loss from using cracked software. Our research presents the following results. First, when network externalities are weak, the monopolist would set a degree of protection which induces existence of software cracking to enhance consumers’ willingness to pay for genuine software by improving network benefits. Conversely, if network externalities are sufficiently strong, then software producer would set a degree of protection which stop software cracking completely. This implies that stopping software cracking is not possible without network effects. Second, if utility loss from using cracked software is severe (mild), then strengthening (weakening) network externalities or lowering (raising) compatibility may reduce the number of consumers using cracked software and increase software producer’s profits consequently. Finally, we show that the monopolistic producer tends to over-protect software when genuine and cracked software are highly compatible or network externalities are relatively weak which results in inadequate consumers using cracked software for social optimum.

This article extends the cost-reducing R&D model with spillovers by d’Aspremont and Jacquemin (1988. “Cooperative and Noncooperative R&D in Duopoly with Spillovers.” The American Economic Review 78: 1133–7, 1990. “Cooperative and Noncooperative R&D in Duopoly with Spillovers: Erratum.” The American Economic Review 80: 641–2) to allow quantity-setting firms (Cournot rivalry) to play the non-cooperative R&D investment decision game with horizontal product differentiation. Unlike Bacchiega, Lambertini, and Mantovani (2010. “R&D-hindering Collusion.” The B.E. Journal of Economic Analysis & Policy 10 (Topics): 66), who identify a parametric region (defined by the extent of technological spillovers and the efficiency of R&D activity), in which the game is a prisoner’s dilemma (self-interest and mutual benefit of cost-reducing innovation conflict), this work shows that product differentiation changes the game into a deadlock (self-interest and mutual benefit do not conflict), regardless of the parameter scale (i.e. also in the absence of spill-over effects ). Then investing in R&D challenges the improvement of interventions aimed at favouring product differentiation. This is because social welfare when firms invest in cost-reducing R&D is greater than when firms do not invest in R&D. Alternatively, R&D subsidies can be used as a social welfare maximising tool also in the absence of R&D spillovers. These results also hold for price-setting firms (Bertrand rivalry).

This paper introduces the impact of online competition to analysis of the urban configuration of a small open city, which was first developed by Alonso (1964. Location and Land Use . Cambridge: Harvard University Press), Mills (1967. “An Aggregative Model of Resource Allocation in a Metropolitan Area.” The American Economic Review 57 (2): 197–210), and Muth (1969. Cities and Housing . Chicago: University of Chicago Press) (AMM hereafter). In comparison to a revised AMM model in Lai and Tsai (2008. “Simplified Alonso-Mills-Muth Model with a Monopoly Vendor.” Journal of Urban Economics 63 (2): 536–43) which assumed a monopoly vendor, the present paper’s online entry brings competition, eventually causes price reduction, city expansion, and asymmetrically ascending land rent, and makes the incumbent vendor relocate to a more remote city boundary. When the disadvantage of online purchasing is not large, the urban configuration demonstrates that most residents purchase online, and only the residents living near the physical vendor make shopping trips. Finally, the benefit of city expansion from online competition eventually goes to the absentee landowners by way of the raised land rents.

We consider the implementation problem for incomplete information and private values. We investigate double implementability of social choice functions in dominant strategy equilibria and ex-post equilibria. We define a new strategic axiom that implies “strategy-proofness” and that is implied by “secure strategy-proofness,” but the converse of these relationships does not hold. We call it “weak secure-strategy-proofness.” We show that a social choice function is doubly implementable if and only if it is weakly securely-strategy-proof .

We study the connection between risk aversion, the number of consumers, and the uniqueness of equilibrium. We consider an economy with two goods and I impatience types, where each type has additive separable preferences with HARA Bernoulli utility function, u H ( x ) ≔ γ 1 − γ b + a γ x 1 − γ ${u}_{\text{H}}(x) := \frac{\gamma }{1-\gamma }{\left(b+\frac{a}{\gamma }x\right)}^{1-\gamma }$ . We show that if γ ∈ 1 , I I − 1 $\gamma \in \left(1,\frac{I}{I-1}\right]$ , the economy has a unique regular equilibrium. Moreover, the methods used, including Newton’s symmetric polynomials and Descartes’ rule of signs, enable us to offer new sufficient conditions for uniqueness in a closed-form expression that highlight the role played by endowments, patience, and specific HARA parameters. Finally, we derive new necessary and sufficient conditions that ensure uniqueness for the particular case of CRRA Bernoulli utility functions with γ = 3.

This paper introduces a family of domains of bargaining problems allowing for non-convexity. For each domain in this family, single-valued bargaining solutions satisfying the Nash axioms are explicitly characterized as solutions of the iterated maximization of Nash products weighted by the row vectors of the associated bargaining weight matrices. This paper also introduces a simple procedure to standardize bargaining weight matrices for each solution into an equivalent triangular bargaining weight matrix, which is simplified and easy to use for applications. Furthermore, the standardized bargaining weight matrix can be recovered from bargaining solutions of simple problems. This recovering result provides an empirical framework for determining the bargaining weights.

We propose a model where two sports leagues compete for sporting talent, and at the same time consider the competitive balance in their domestic championships. The allocation of broadcasting revenues by the league-governing body acts as an incentive for teams to invest in talent. We derive a strategic league authority’s optimal sharing rule of broadcasting revenues across teams in the league. While a weighted form of performance-based sharing is the best way of attracting talent, cross-subsidization from high- to low-payroll teams is required to improve competitive balance. The optimal sharing rule is then a combination of these two “sub-rules”. We show that the distribution of broadcasting revenues in two first divisions in European men’s football, the English Premier League (EPL) and the French Ligue 1 (L1), corresponds to the optimal sharing rule we discuss. We propose a new method to assess empirically the cross-subsidization impact of the sharing formula. As the impact of cross-subsidization is greater in the EPL than L1, we conclude that ensuring domestic competitive balance seems to be a more important target for the EPL than for L1.

Inspired by Zhao, J. 1996. “The Hybrid Equilibria and Core Selection in Exchange Economies with Externalities.” Journal of Mathematical Economics 26 (4): 387–407, Askoura, Y. 2011. “The Weak-Core of a Game in Normal Form with a Continuum of Players.” Journal of Mathematical Economics 47: 43–7, Askoura, Y. 2017. “On the Core of Normal Form Games with a Continuum of Players.” Mathematical Social Sciences 89: 32–42, Yang, Z. 2020. “The Weak α-core of Exchange Economies with a Continuum of Players and Pseudo-utilities.” Journal of Mathematical Economies 91: 43–50 and Yang, Z., and X. Zhang. 2021. “A Weak α-core Existence Theorem of Games with Nonordered Preferences and a Continuum of Agents.” Journal of Mathematical Economics 94: 102464, we establish an exchange economy with externalities and a continuum of agents. We define the weak hybrid equilibrium in this model and prove the existence theorem under the regular conditions. Furthermore, we analyze the relation between the set of hybrid equilibria and the set of competitive equilibria in an exchange economy without externalities and with a continuum of agents.

I model a competitive labor market in which agents of different skill levels decide whether to enter the market as a manager or as a worker. After roles are chosen, a two-sided matching market is realized and a cooperative assignment game occurs. There exists a unique rational expectations equilibrium that induces a stable many-to-one matching and wage structure. Positive assortative matching occurs if and only if the production function exhibits a condition that I call role supermodularity , which is stronger than the strict supermodularity condition commonly used in the matching literature because a high skilled agent with a role choice is only willing to enter the market as a worker if she expects that it is more profitable to cluster with only other high skilled agents than to exclusively manage. The wage structure in equilibrium is consistent with empirical evidence that the wage gap is driven both by increased within-firm positive sorting as well as between-firm segregation.

It is a well-established property that more precise private information leads to lower non-fundamental volatility in a coordination economy with dispersed information. In this note, we identify conditions under which such an argument holds or does not hold. In particular, we show that the opposite relationship holds when (1) there is a strong positive correlation between private information of different agents and (2) public information is endogenously generated.

This study demonstrates why traditional “cost-saving” technical progress fails in an economy where consumption is time-constrained. In such a case, introducing “time-saving” technical progress establishes a new consumption-production equilibrium characterized by higher per-capita consumption and real income, lower prices, and, a higher scale of production for surviving producers. Nonetheless, since there is a limit to how much time can be saved by technological advances, the model also suggests an alternative solution in the form of a rising labor force (say via immigration) to close the production-consumption gap. This solution generates an unambiguous increase in welfare, vis-à-vis cost-reducing or time-saving technical progress.