Long-term fairness with bounded worst-case losses

Balan, Gabriel; Richards, Dana; Luke, Sean

doi:10.1007/s10458-009-9106-9

Cited by 8 publications

(4 citation statements)

References 18 publications

(12 reference statements)

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“…conventions with smaller price of anonymity). In general, finding an optimal convention is an NP-hard problem (Balan, Richards, and Luke 2011), but for a more restricted set of infinitely repeated resource allocation games, we might be able to find the optimal convention, similar to the Thue-Morse sequence (Richman 2001) used by (Kuzmics, Palfrey, and Rogers 2010) in the Nash demand game.…”

Section: Discussionmentioning

confidence: 99%

Symmetric Subgame Perfect Equilibria in Resource Allocation

Cigler

Faltings

2021

AAAI

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We analyze symmetric protocols to rationally coordinate on an asymmetric, efficient allocation in an infinitely repeated N-agent, C-resource allocation problems. (Bhaskar 2000) proposed one way to achieve this in 2-agent, 1-resource allocation games: Agents start by symmetrically randomizing their actions, and as soon as they each choose different actions, they start to follow a potentially asymmetric "convention" that prescribes their actions from then on. We extend the concept of convention to the general case of infinitely repeated resource allocation games with N agents and C resources. We show that for any convention, there exists a symmetric subgame perfect equilibrium which implements it. We present two conventions: bourgeois, where agents stick to the first allocation; and market, where agents pay for the use of resources, and observe a global coordination signal which allows them to alternate between different allocations. We define price of anonymity of a convention as the ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the convention. We show that while the price of anonymity of the bourgeois convention is infinite, the market convention decreases this price by reducing the conflict between the agents.

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Section: Discussionmentioning

confidence: 99%

Symmetric Subgame Perfect Equilibria in Resource Allocation

Cigler

Faltings

2021

AAAI

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“…conventions with smaller price of anonymity). In general, finding an optimal convention is an NP-hard problem (Balan, Richards, & Luke, 2011), but for a more restricted set of infinitely repeated resource allocation games, we might be able to find the optimal convention, similar to the Thue-Morse sequence (Richman, 2001) used by Kuzmics et al (2010) in the Nash demand game.…”

Section: Discussionmentioning

confidence: 99%

Symmetric Subgame-Perfect Equilibria in Resource Allocation

Cigler

Faltings

2014

jair

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We analyze symmetric protocols to rationally coordinate on an asymmetric, efficient allocation in an infinitely repeated N -agent, C-resource allocation problems, where the resources are all homogeneous. Bhaskar proposed one way to achieve this in 2-agent, 1-resource games: Agents start by symmetrically randomizing their actions, and as soon as they each choose different actions, they start to follow a potentially asymmetric "convention" that prescribes their actions from then on. We extend the concept of convention to the general case of infinitely repeated resource allocation games with N agents and C resources. We show that for any convention, there exists a symmetric subgame-perfect equilibrium which implements it. We present two conventions: bourgeois, where agents stick to the first allocation; and market, where agents pay for the use of resources, and observe a global coordination signal which allows them to alternate between different allocations. We define price of anonymity of a convention as a ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the subgame-perfect equilibrium which implements the convention. We show that while the price of anonymity of the bourgeois convention is infinite, the market convention decreases this price by reducing the conflict between the agents.

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“…In our case agents have static and heterogeneous preferences, instead of demands, over multiple items, and the sets of agents and items is fixed. Balan et al [4] also study the repeated allocation of items (i.e., courses assigned to professors), but they focus on the average of utilities received by the agents for a sequence of allocations.…”

Section: Allocations?"mentioning

confidence: 99%

Fair allocation of a multiset of indivisible items

Gorantla¹,

Marwaha²,

Velusamy³

2023

Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

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The problem of fairly allocating a set of indivisible items is a well-known challenge in the field of (computational) social choice. In this scenario, there is a fundamental incompatibility between notions of fairness (such as envy-freeness and proportionality) and economic efficiency (such as Pareto-optimality). However, in the real world, items are not always allocated once and for all, but often repeatedly. For example, the items may be recurring chores to distribute in a household. Motivated by this, we initiate the study of the repeated fair division of indivisible goods and chores and propose a formal model for this scenario. In this paper, we show that, if the number of repetitions is a multiple of the number of agents, we can always find (i ) a sequence of allocations that is envy-free and complete (in polynomial time), and (ii ) a sequence of allocations that is proportional and Pareto-optimal (in exponential time). On the other hand, we show that irrespective of the number of repetitions, an envy-free and Pareto-optimal sequence of allocations may not exist. For the case of two agents, we show that if the number of repetitions is even, it is always possible to find a sequence of allocations that is overall envy-free and Pareto-optimal. We then prove even stronger fairness guarantees, showing that every allocation in such a sequence satisfies some relaxation of envy-freeness.

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Long-term fairness with bounded worst-case losses

Cited by 8 publications

References 18 publications

Symmetric Subgame Perfect Equilibria in Resource Allocation

Symmetric Subgame Perfect Equilibria in Resource Allocation

Symmetric Subgame-Perfect Equilibria in Resource Allocation

Fair allocation of a multiset of indivisible items

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