Arthur Dolgopolov

Working papers

Revealed Social Preferences

(with Mikhail Freer)

We apply a revealed preference approach to test the consistency of observed behavior with theories of social preferences. In particular, we provide revealed preference criteria for the observed set of choices generated by inequality averse preferences and by other-regarding preferences that exhibit increasing benevolence. We further apply these tests to experimental data on dictator games. Finally, we show how to apply constructed tests to other games commonly used to study social preferences, including ultimatum, investment and carrot-stick games.

Work in progress

Revealed Markov Strategies

(with Mikhail Freer)

Major problem with identification of strategies in the repeated games is the vastness of strategy space stemming from dependence on history (previous actions). Moreover, strategies can be of different complexity (depending on length of histories they use). In addition, there are two competing representations: a function of history and a finite automaton. We provide methodology for partial identification of strategies in repeated games for both representations. Moreover, we show that minimum complexity of a strategy that explains player's behavior can be efficiently found. In addition, we characterize a strict subset of finite automatons isomorphic to the set of history-dependent strategies. Finally, we illustrate the method using the experimental data on repeated prisoner's dilemma.

Bayesian Nash Revealed

(with Mikhail Freer and Marco Castillo)

We study games of incomplete information from a revealed preference perspective and provide a nonparametric test for Bayesian Nash rationalization - existence of such expected utility representations for agents that observed choices are Bayesian Nash equilibria. In the basic setup we assume that everything, but the cardinal utility is known by the researcher (including beliefs of players over distribution of types). However, we discuss the possibility of relaxing several assumptions. In particular, we consider that researcher may be unaware of the distribution of types, or number of types. The test can also be applied with assumptions about rationality of agents that follow different theories of behavior under risk - cumulative propsect theory or rank-dependent expected utility.

Winner Determination in Combinatorial Auctions with Public and Private Goods and OR* Preferences

(with Daniel Houser and Weiwei Zheng)

We present an efficient linear program that can be used to solve winner determination problem for combinatorial auction in a market with both private and public goods. The setting can be applied to voters bidding in an interpretive environment with a propositional logic bidding language. We allow for a wide set of constraints, complement and substitute relations, and discuss several Cumulative Utility Functions. Solving the winner determination problem as a linear program proves to have a large computational advantage over other methods, which is valuable due to problem being generally NP-complete. We confirm this result with in silico experiments.

Equitable Sequencing and Allocation Under Uncertainty

The paper uses Thue-Morse sequence and knapsack problem to formally relate several problems of negotiations, fair division and tournament sequencing. All of the considered problems are shown to be reduced versions of partitioning problem, i.e. equally dividing items into two sets. An argument is made that it is often beneficial to set the partitioning problem as stochastic with item values drawn from a distribution, especially but not limited to the case of intangible items like skill level. Balanced alternation according to Thue-Morse sequence proves to be the better mechanic in this case for all sample sizes for common distributions. This is not true for all distributions and for settings with k>2 agents. A further improvement upon this mechanic is greedy approximation over the underlying subset-sum problem.

On Welfare Losses in Constrained School Choice

(with Mikhail Freer)