This paper examines a normal form game of network formation due to Myerson (Game theory: analysis of conflict, Harvard University Press, Cambridge, 1991). All players simultaneously announce the links they wish to form. A link is created if and only if there is mutual consent for its formation. The empty network is always a Nash equilibrium of this game. We define a refinement of Nash equilibria that we call trial perfect. We show that the set of networks which can be supported by a pure strategy trial perfect equilibrium coincides with the set of pairwise-Nash equilibrium networks, for games with link-responsive payoff functions.
We study the salience and power of reference points in determining the effective anchors and aspirations in bargaining problems. Along this line, we enrich the analysis of the standard bargaining model with two new parameters: the first parameter can be interpreted as the effectiveness (or salience) of the reference point in determining the anchor, whereas the second parameter can be interpreted as its effectiveness in shaping agents' aspirations. Utilizing these parameters, we provide a unifying framework for the study of bargaining problems with a reference point. The two-parameter family of bargaining solutions we obtain encompasses some well-known solutions as special cases. We offer multiple characterizations for each individual member of this family as well as two characterizations for the whole solution family in bilateral bargaining problems.
We study one-sided matching problem, also known as roommate problem, where a group of people need to be paired in order to be assigned to certain rooms. We assume that number of rooms are limited and thus no one can be by himself. Each student has strict preferences over their roommates. Central notion in this problem is stability. We consider exchange-stability of Alcalde (Econ Des 1:275-287, 1995), which is immune to group of students exchanging their rooms/roommates with each other. He shows that exchange-stable matching may not always exist and considers specific domains of preferences to guarantee existence of such matching. We define more general domains of preferences on which exchange-stable matching is guaranteed to exist.
This paper investigates the implications of the unequal division of the domestic labor in men and women's participation and effort incentives in competitive relations, in which the labor market is the main example. We found that moderate levels of affirmative action (i.e., bias in favor of women) incentivize men and women to exert more effort and women's participation. However, it cannot guarantee full participation and equal effort among men and women without inducing economic inefficiency or even distorting the labor market. Given these limitations, we consider the effects of an alternative policy that supports the men's involvement in the domestic tasks. The main conclusion is that if we want men and women to have the same opportunities in the labor market, we must solve the household problem first. While women hold a larger share of the domestic labor, they are in a weaker position to compete with men. We expect that our findings will guide researchers and decision-makers implementing effective policies that can allow men and women to have the same labor market opportunities.
Jean-Charles de Borda introduced the Borda rule with the motivation of avoiding the so-called pairwise-majority-loser. We revisit this topic by examining the uniqueness of the Borda rule as a scoring rule that is consistent with the pairwise-majority-loser criterion. We first show that this uniqueness does not hold for any fixed population. In fact, when there are three alternatives and six voters, all scoring rules are consistent with the pairwise-majority-loser criterion. We then show that for each non-Borda scoring rule, there exists a population n such that the rule is not consistent with this criterion for all populations of size larger than n.
Asymmetric information can lead to inefficient outcomes in many bargaining contexts. It is sometimes natural to think of asymmetric information as emerging from imperfect observation of previously taken actions (e.g., obtaining compliments or substitutes for the item being bargained over). How do such strategic investment choices prior to bargaining interact with the strategic problem of bargaining under private information? We focus on bilateral bargaining when players can make unobserved investments in the value of the item prior to their interaction. With two-sided hidden investment, strategic uncertainty induces a post-investment problem analogous to that in Myerson and Satterthwaite (J Econ Theory 29(2):265–281, 1983), and inefficiencies might be expected to arise. But, there are strong incentives to avoid investment levels that do not lead to trade and this must be anticipated by the other trader. This effect is shown to drive a form of unraveling; as a result in every equilibrium to the larger game the good ends up in the hands of the agent with the higher valuation.
We study two-stage elimination Tullock contests. In the first stage all the players compete against each other; then some advance to the second stage while the others are removed. The finalists compete against each other in the second stage, and one of them wins the prize. To maximize the expected total effort, the designer can give a head start to the winner of the first stage when he competes against the other finalists in the second stage. We show that the optimal head start, independent of the number of finalists, always increases the players’ expected total effort. We also show how the number of players and finalists affect the value of the optimal head start.
The Nash axiom is a basic property of consistency in choice. This paper proposes weaker versions of the axiom and examines their logical implications. In particular, we demonstrate that weak Nash axioms are useful to understand the relationship between the Nash axiom and the path independence axiom. We provide an application of weak Nash axioms to the no-envy approach. We present a possibility result and an impossibility result.
We provide a respecification of an integer programming characterization of Arrovian social welfare functions introduced by Sethuraman et al. (Math Oper Res 28:309–326, 2003). By exploiting this respecification, we give a new and simpler proof of Theorem 2 in Kalai and Muller (J Econ Theory 16:457–469, 1977).
This study analyzes the equilibrium of a core-selecting package auction under incomplete information. The ascending proxy auction of Ausubel and Milgrom (Front Theor Econ 1:1–42, 2002) is considered in a stylized environment with two goods, two local bidders, and one global bidder. Local bidders shade bids in the equilibrium because of the free-riding incentive. We examine the effect of reserve prices. We show that a reserve price for individual goods increases the equilibrium local bids, whereas they may be decreased by a reserve price for the package of goods. A flexible non-monotonic reserve price rule can improve allocative efficiency as well as seller revenue in the equilibrium.
We provide a respecification of an integer programming characterization of Arrovian social welfare functions introduced by Sethuraman et al. (Math Oper Res 28:309-326, 2003). By exploiting this respecification, we give a new and simpler proof of Theorem 2 in Kalai and Muller (J Econ Theory 16:457-469, 1977).
Suppose that a group of agents have demands for some good. Every agent owns a technology which allows them to produce the good, with these technologies varying in their effectiveness. If all technologies exhibit increasing returns to scale (IRS) then it is always efficient to centralize production of the good, whereas efficiency in the case of decreasing returns to scale (DRS) typically requires to spread production. We search for stable cost allocations while differentiating allocations with homogeneous prices, in which all units produced are traded at the same price, from allocations with heterogeneous prices. For the respective cases of IRS or DRS, it is shown that there always exist stable cost sharing rules with homogeneous prices. Finally, in the general framework (under which there may exist no stable allocation at all) we provide a sufficient condition for the existence of stable allocations with homogeneous prices. This condition is shown to be both necessary and sufficient in problems with unitary demands.
The existing models of mixed public–private school systems usually capture only the decreasing average cost faced by public schools, whereas empirical studies find evidence of it for private schools as well. Motivated by this, an equilibrium model of a mixed public–private school system is studied in this paper, whereby private schools also face decreasing average cost over enrollment. In the model, households, heterogeneous with respect to exogenously specified income and child’s ability, choose among a public and a private school. Private school charges tuition whereas public school is free. Public school spending is financed by income tax revenue collected from all households and the tax rate is determined via majority voting. Achievement of a child depends on its ability and education spending. Under the assumptions on the parameters of the model, a joint lognormal distribution of income and ability, and a Cobb–Douglas utility, majority voting equilibrium is numerically shown to exist. The model is calibrated to match certain statistics from the 2013 Turkish data. Using the calibrated model, we compare the benchmark for a mixed public–private school system with a pure public school system to understand the impact of shutting down some of the private schools in Turkey following the July 15 coup attempt. We find that mean achievement and variance of achievement after high school is $$0.039\%$$ 0.039% higher and $$0.013\%$$ 0.013% lower respectively in a pure public school system.