Parimal Kanti Bag

Multi-stage voting, sequential elimination and Condorcet consistency

A class of voting procedures based on repeated ballots and elimination of one candidate in each round is shown to always induce an outcome in the top cycle and is thus Condorcet consistent, when voters behave strategically. This is an important class as it covers multi-stage, sequential elimination extensions of all standard one-shot voting rules (with the exception of negative voting), the same one-shot rules that would fail Condorcet consistency. The necessity of repeated ballots and sequential elimination are demonstrated by further showing that Condorcet consistency would fail in all standard voting rules that violate one or both of these conditions.

Optimal auction design and R&D

Abstract An indivisible object is to be procured through bidding from one of two prospective suppliers. Firms decide whether to invest in cost-reduction before the bidding. The procurer commits to a mechanism ahead of investment decisions by firms. If the procurer can charge entry fees that may be discriminatory, a sealed-bid second-price auction uniquely implements the first-best outcome and is optimal for the buyer. ‘Revenue Equivalence’ holds when first-best investments are symmetric; however, it breaks down when first-best investments are asymmetric. Without entry fees, the procurer may want to bid-discriminate between ex-ante identical firms to induce the favored firm to invest and become strong while the unfavored firm not to invest and stay weak. This result runs counter to the earlier findings on discrimination in procurement auctions without pre-contract R&D: the principal favors the weaker agent to induce stronger bid competition.

Strategic information revelation in fundraising

Abstract We consider a model of voluntary contributions for a public project with random number of potential contributors. The fundraiser, who observes this number, has to decide whether to reveal or suppress the information before contributions are given. The fundraiser’s objective is to collect maximal contributions. We show that whether the public project is convex or non-convex can be the key to the fundraiser’s announcement decision. In the convex case, this number is always revealed. In the non-convex case the number may not be revealed at all or sometimes revealed only when it is in an intermediate range. In the presence of multiple equilibria, total contributions increase with the extent of concealment.

On Sequential and Simultaneous Contributions under Incomplete Information

When contributors to a common cause (or public good) are uncertain about each others’ valuations, early contributors are likely to be cautious in free-riding on future contributors. Contrary to the case of complete information, when contributors have independent private valuations for the public good, the expected total contribution generated in a sequential move game may be higher than in a simultaneous move game. This is established in a conventional framework with quasi-linear utility where agents care only about the total provision of the public good (rather than individual contribution levels) and there is no non-convexity in the provision of the public good. We allow for arbitrary number of agents and fairly general distribution of types.

Match-fixing under competitive odds

Two bookmakers compete in Bertrand fashion while setting odds on the outcomes of a sporting contest where an influential punter (or betting syndicate) may bribe some player(s) to fix the contest. Zero profit and bribe prevention may not always hold together. When the influential punter is quite powerful, the bookies may coordinate on prices and earn positive profits for fear of letting the ‘lemons’ (i.e., the influential punter) in. On the other hand, sometimes the bookies make zero profits but also admit match-fixing. When match-fixing occurs, it often involves bribery of only the strong team. The theoretical analysis is intended to address the problem of growing incidence of betting related corruption in world sports including cricket, horse races, tennis, soccer, basketball, wrestling, snooker, etc.

Repeated Charitable Contributions under Incomplete Information

Incomplete information about (independent) private valuations of charities by potential donors provides an important strategic rationale for announcement of donations during fundraising drives and explains why donors may add to their initial contributions after learning about contributions made by others. In a two-stage fundraising drive where potential donors may contribute at either or both stages, it is shown that under certain conditions, announcement of contributions generates higher expected total contribution. Contribution announcement plays a similar positive role even when the charity acquires information about donor valuations prior to actual fundraising and can take actions to mitigate incomplete information among donors. Copyright 2008 The Author(s). Journal compilation Royal Economic Society 2008.

Peer Transparency In Teams: Does It Help Or Hinder Incentives?

In a joint project involving two players of a two‐round effort investment game with complementary efforts, transparency, by allowing players to observe each other’s efforts, achieves at least as much, and sometimes more, collective and individual efforts relative to a nontransparent environment. Without transparency multiple equilibria can arise, and transparency eliminates the inferior equilibria. When full cooperation arises only under transparency, it occurs gradually: No worker sinks in the maximum amount of effort in the first round, preferring instead to smooth out contributions over time. If the players’ efforts are substitutes, transparency makes no difference to equilibrium efforts.

Distributing awards efficiently: More on King Solomon's problem

We consider a multi-award generalisation of King Solomon’s problem: k identical and indivisible awards should be distributed among agents, k 1) prizes efficiently in sub-game perfect equilibria without any monetary transfers in equilibrium. Finally, in the multi-awards case we relax the complete information assumption and achieve implementation of efficient allocation by iterative elimination of weakly dominated strategies, using generalisation of Olszewski’s (2003) mechanism.

Match-Fixing in a Monopoly Betting Market

A monopolist bookmaker may set betting odds on a fairly even contest to induce match-fixing by an influential corrupt punter. His loss to the corrupt punter is more than made up for by enticing enough ordinary punters to bet on the losing team. This result is in sharp contrast to competitive bookmaking, where even contests have been shown to be immune to fixing. The analysis also reveals a surprising result that the incidence of match-fixing can dramatically fall when match-fixing opportunities rise. This is shown by comparing two scenarios—when only one team is corruptible and when both are corruptible. For both teams corruptible, the bookmaker is uncertain about to which team the influential punter will have access, so carefully maneuvering the odds to induce match-fixing is too costly.

Corrupt Bookmaking in a Fixed Odds Illegal Betting Market

Illegal betting in a two-team sports contest is studied with player sabotage instigated by a monopolist bookmaker. Whereas punters hold beliefs about the teams’ winning chances correlated with Natures draw, the bookmakers information is noise-free. Enforcement investigates with a higher probability, the greater the upset. In such an environment, if punters do not suspect match-fixing, the favourite is bribed, thus creating upsets and intensifying subsequent investigations. Match-fixing continues to hold even when punters are rational, provided that the bookies beliefs are noisy: the bookie bribes the team he thinks is the favourite and the bettors bet on their perceived favourites.