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on Game Theory |
| By: | Subhasish M. Chowdhury (School of Economics, Centre for Behavioural and Experimental Social Science, and Centre for Competition Policy, University of East Anglia); Dan Kovenock (Economic Science Institute, Chapman University); David Rojo Arjona (Department of Economics, University of Leicester); Nathaniel T. Wilcox (Economic Science Institute, Chapman University) |
| Abstract: | This article examines behavior in two-person constant-sum Colonel Blotto games in which each player maximizes the expected total value of the battlefields won. A lottery contest success function is employed in each battlefield. Recent experimental research on such games provides only partial support for Nash equilibrium behavior. We hypothesize that the salience of battlefields affects strategic behavior (the salient target hypothesis). We present a controlled test of this hypothesis – against Nash predictions – when the sources of salience come from certain asymmetries in either battlefield values or labels (as in Schelling (1960)). In both cases, subjects over-allocate the resource to the salient battlefields relative to the Nash prediction. However, the effect is stronger with salient values. In the absence of salience, we replicate previous results in the literature supporting the Nash prediction. |
| Keywords: | Conflict, Experiment, Colonel Blotto, Focal point, Asymmetry |
| JEL: | C72 C91 D72 D74 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:16-16&r=gth |
| By: | David Kelsey (Department of Economics, University of Exeter); Sara le Roux (Department of Economics, Oxford Brookes University) |
| Abstract: | We conducted a set of experiments to compare the effect of ambiguity in single person decisions and games. Our results suggest that ambiguity has a bigger impact in games than in ball and urn problems. We ?nd that ambiguity has the opposite effect in games of strategic substitutes and complements. This con?rms a theoretical prediction made by Eichberger and Kelsey (2002). The experiments also test whether subjects' ?perception of ambiguity differs when faced by a local opponent as opposed to a foreign one. Our results show that there is little evidence of more in?uence of ambiguity on behaviour when faced by foreign subjects. |
| Keywords: | Ambiguity; Choquet expected utility; strategic complements; strategic substitutes; Ellsberg urn. |
| JEL: | C72 C91 D03 D81 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:exe:wpaper:1605&r=gth |
| By: | Candogan, Ozan (University of Chicago); Epitropou, Markos (University of Pennsylvania); Vohra, Rakesh V. (University of Pennsylvania) |
| Abstract: | Under full substitutability of preferences, it has been shown that a competitive equilibrium exists in trading networks,and is equivalent (after a restriction to equilibrium trades) to (chain) stable outcomes. In this paper, we formulate the problem of finding an efficient outcome as a generalized submodular flow problem on a suitable network. Equivalence with seemingly weaker notions of stability follows directly from the optimality conditions, in particular the absence of improvement cycles in the flow problem. Our formulation yields strongly polynomial algorithms for finding competitive equilibria in trading networks, and testing (chain) stability. |
| Keywords: | Trading networks, competitive equilibrium, stability, submodular flow problems, discrete convexity |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:323&r=gth |
| By: | Anna Bogomolnaia (National Research University Higher School of Economics); Herve Moulin (National Research University Higher School of Economics); Fedor Sandomirskiy (National Research University Higher School of Economics); Elena Yanovskaya (National Research University Higher School of Economics) |
| Abstract: | The Competitive Equilibrium with Equal Incomes is an especially appealing ecient and envy-free division of private goods when utilities are additive: it maximizes the Nash product of utilities and is single-valued and continuous in the marginal rates of substitution. The CEEI to divide bads captures similarly the critical points of the Nash product in the ecient frontier. But it is far from resolute, allowing routinely many divisions with sharply di erent welfare consequences. Even the much more permissive No Envy property is profoundly ambiguous in the division of bads: the set of ecient and envy-free allocations can have many connected components, and has no single-valued selection continuous in the marginal rates. The CEEI to divide goods is Resource Monotonic (RM): everyone (weakly) bene ts when the manna increases. But when we divide bads eciently, RM is incompatible with Fair Share Guarantee, a much weaker property than No Envy. |
| Keywords: | fair division of goods, fair division of bads, competitive equilibrium with equal incomes, Nash product, envy-freeness, resource monotonicity, independence of lost bids. |
| JEL: | D61 D63 D82 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:147/ec/2016&r=gth |
| By: | Battal Dogan; Bettina Klaus |
| Abstract: | Which mechanism to use to allocate school seats to students still remains a question of hot debate. Meanwhile, immediate acceptance mechanisms remain popular in many school districts. We formalize desirable properties of mechanisms when respecting the relative rank of a school among the students' preferences is crucial. We show that those properties, together with well-known desirable resource allocation properties, characterize immediate acceptance mechanisms. Moreover, we show that replacing one of the properties, consistency, with a weaker property, non-bossiness, leads to a characterization of a much larger class of mechanisms, which we call choice-based immediate acceptance mechanisms. It turns out that certain objectives that are not achievable with immediate acceptance mechanisms, such as affirmative action, can be achieved with a choice-based immediate acceptance mechanism. |
| Keywords: | affirmative action; consistency; favoring-higher-ranks; immediate acceptance mechanism; non-bossiness; non-wastefulness; rank-respecting unavailable-type-invariance; resource-monotonicity. |
| JEL: | C71 C78 D61 D71 |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:16.15&r=gth |
| By: | Luis Alcala; Fernando Tohme; Carlos Dabus |
| Abstract: | We study the interaction between strategy, heterogeneity and growth in a two-agent model of capital accumulation. Preferences are represented by recursive utility functions with decreasing marginal impatience. The stationary equilibria of this dynamic game are analyzed under two alternative information structures: one in which agents precommit to future actions, and another one where agents use Markovian strategies. In both cases, we develop sufficient conditions to prove the existence of equilibria and characterize their stability properties. The precommitment case is characterized by monotone convergence, but Markovian equilibria may exhibit nonmonotonic paths, even in the long-run. |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1608.06959&r=gth |
| By: | Doraszelski, Ulrich; Escobar, Juan |
| Abstract: | The timing of decisions is an essential ingredient in modelling any strategic situation. Yet, determining the most realistic and appropriate protocol of moves can be challenging. We introduce a class of dynamic stochastic games that we call separable dynamic games with noisy transitions and establish that they are protocol invariant provided that periods are sufficiently short. Protocol invariance means that the set of Markov perfect equilibria is nearly the same irrespective of the order in which players are assumed to move within a period. We also show that the equilibria have a remarkably simple structure. |
| Keywords: | Dynamic games; Markov perfect equilibrium; Protocol of moves |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11447&r=gth |
| By: | Lincove, Jane Arnold (University of Maryland, Baltimore County); Cortes, Kalena E. (Texas A&M University) |
| Abstract: | We examine the role of information in the college matching behavior of low- and high-income students, exploiting a state automatic admissions policy that provides some students with perfect a priori certainty of college admissions. We find that admissions certainty encourages college-ready low-income students to seek more rigorous universities. Low-income students who are less college-ready are not influenced by admissions certainty and are sensitive to college entrance exams scores. Most students also prefer campuses with students of similar race, income, and high school class rank, but only highly-qualified low-income students choose institutions where they have fewer same-race and same-income peers. |
| Keywords: | academic undermatching and overmatching, social matching, admissions policies, Texas Top 10% Plan, automatic admissions |
| JEL: | I21 I23 J15 |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp10150&r=gth |
| By: | Nathaniel T. Wilcox (Economic Science Institute, Chapman University) |
| Abstract: | For simple prospects of the kind routinely used for certainty equivalent elicitation, random expected utility preferences imply a conditional expectation function that can mimic deterministic rank dependent preferences. That is, an agent with random expected utility preferences can have mean certainty equivalents that look exactly like rank dependent probability weighting functions of the inverse-s shape discussed by Quiggin (1982) and later advocated by Tversky and Kahneman (1992) and other scholars. It seems that certainty equivalents cannot nonparametrically identify preferences, at least not in every relevant sense, since their conditional expectation depends on assumptions concerning the source and nature of their variability. |
| Keywords: | Random Expected Utility, Certainty Equivalents, Money Equivalents, Probability Weighting, Probability Weighting Function, Weighting Function |
| JEL: | C13 C91 D81 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:16-14&r=gth |
| By: | Samuel Häfner; Georg Nöldeke (University of Basel) |
| Abstract: | This paper analyzes iterated incumbency contests with heterogeneous valuations in a large population setting. Incumbents repeatedly face di erent challengers, holding on to their positions until defeated in a contest. Defeated incumbents turn into challengers until they win a contest against an incumbent, thereby regaining an incumbency position. We consider steady-state equilibria of this process and study how and to which extend individuals sort into the incumbency positions depending on their valuations. In particular, we identify sucient conditions for positive sorting, meaning that the share of individuals with a given valuation holding an incumbency position is increasing in the valuation, and provide an example to show that negative rather than positive sorting may arise in equilibrium. Further results show how incumbency rents and sorting are a ected by the frequency at which incumbency is contested and the scarcity of the incumbency positions. |
| Keywords: | Contests, Sorting, Incumbency Rents, Steady-State Equilibrium |
| JEL: | C72 D72 D74 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:bsl:wpaper:2016/02&r=gth |