Contest Design with Threshold Objectives

Elkind, Edith; Ghosh, Abheek; Goldberg, Paul W.

doi:10.2139/ssrn.4155267

Cited by 3 publications

(2 citation statements)

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“…Two very recent related papers are by Birmpas et al [9] and Elkind et al [17]. Both these papers do not have activities, i.e., the players produce output directly for the contests, which makes their models a bit different (simpler) than ours, but they add complexity along other dimensions.…”

Section: Related Workmentioning

confidence: 99%

“…Birmpas et al [9] have both budgets and costs in the same model, and they give a constant factor PoA bound by augmenting players' budgets when computing the equilibrium welfare (but not when computing the optimal welfare). Elkind et al [17] consider a model with only one contest and in the case of incomplete information. Their focus is on mechanism design, and for one of the objectives studied in the paper, they prove that the optimal contest distributes its prize equally to all players who produce output above some threshold, similar to the contests in our paper.…”

Section: Related Workmentioning

confidence: 99%

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Simultaneous Contests with Equal Sharing Allocation of Prizes: Computational Complexity and Price of Anarchy

Elkind¹,

Ghosh²,

Goldberg³

2022

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We study a general scenario of simultaneous contests that allocate prizes based on equal sharing: each contest awards its prize to all players who satisfy some contest-specific criterion, and the value of this prize to a winner decreases as the number of winners increases. The players produce outputs for a set of activities, and the winning criteria of the contests are based on these outputs. We consider two variations of the model: (i) players have costs for producing outputs; (ii) players do not have costs but have generalized budget constraints. We observe that these games are exact potential games and hence always have a pure-strategy Nash equilibrium. The price of anarchy is 2 for the budget model, but can be unbounded for the cost model. Our main results are for the computational complexity of these games. We prove that for general versions of the model exactly or approximately computing a best response is NP-hard. For natural restricted versions where best response is easy to compute, we show that finding a pure-strategy Nash equilibrium is PLS-complete, and finding a mixed-strategy Nash equilibrium is (PPAD∩PLS)-complete. On the other hand, an approximate pure-strategy Nash equilibrium can be found in pseudo-polynomial time. These games are a strict but natural subclass of explicit congestion games, but they still have the same equilibrium hardness results.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%