arXiv subjects

Debapriya Sen

Publications and source records attributed to Debapriya Sen.

4 recordsLinked to original sources

arXiv2026

Incidence Bimatrix Games

We solve a natural bimatrix game related to graphs. We consider a finite directed graph $G=(V,E),$ where the strategy set of Player I is the set of vertices $V$ and that of Player II is the set of edges $E.$ There are two sets of positive weights ${\{\alpha_e\}}_{e\in E}$ and ${\{\beta_e\}}_{e\in E}.$ If Player I chooses a vertex $v$ and Player II chooses an edge $e,$ then the payoff to both players is zero if $v$ and $e$ are not incident. If $e$ originates from $v,$ then Player I obtains $\alpha_e$ and Player II obtains $-\beta_e.$ If $e$ terminates at $v,$ then Player I obtains $-\alpha_e$ and Player II obtains $\beta_e.$ For this game the payoff matrices are weighted incidence matrices of the graph $G.$ We show that when the graph is acyclic, Player I has a unique strategy in any equilibrium. At this strategy, every vertex is chosen with a probability that is proportional to the maximum length over all directed paths originating from that vertex. Defining the path matrix of the graph, it is shown that the set of all equilibrium strategies of Player II is the convex hull of the column vectors of the path matrix. This work extends earlier results of Bapat and Tijs (1997) for zero-sum games.

econ.TH↗

arXiv2022

On mechanism design with expressive preferences: an aspect of the social choice of Brexit

We study some problems of collective choice when individuals can have expressive preferences, that is, where a decision-maker may care not only about the material benefit from choosing an action but also about some intrinsic morality of the action or whether the action conforms to some identity-marker of the decision-maker. We construct a simple framework for analyzing mechanism design problems with such preferences and present some results focussing on the phenomenon we call "Brexit anomaly". The main findings are that while deterministic mechanisms are quite susceptible to Brexit anomaly, even with stringent domain restriction, random mechanisms assure more positive results.

econ.TH↗

arXiv2021

A characterization of lexicographic preferences

This paper characterizes lexicographic preferences over alternatives that are identified by a finite number of attributes. Our characterization is based on two key concepts: a weaker notion of continuity called 'mild continuity' (strict preference order between any two alternatives that are different with respect to every attribute is preserved around their small neighborhoods) and an 'unhappy set' (any alternative outside such a set is preferred to all alternatives inside). Three key aspects of our characterization are: (i) use of continuity arguments, (ii) the stepwise approach of looking at two attributes at a time and (iii) in contrast with the previous literature, we do not impose noncompensation on the preference and consider an alternative weaker condition.

econ.TH↗

arXiv2018

$k$th price auctions and Catalan numbers

This paper establishes an interesting link between $k$th price auctions and Catalan numbers by showing that for distributions that have linear density, the bid function at any symmetric, increasing equilibrium of a $k$th price auction with $k\geq 3$ can be represented as a finite series of $k-2$ terms whose $\ell$th term involves the $\ell$th Catalan number. Using an integral representation of Catalan numbers, together with some classical combinatorial identities, we derive the closed form of the unique symmetric, increasing equilibrium of a $k$th price auction for a non-uniform distribution.

econ.TH↗