Automated Synthesis of Mechanisms

Mittelmann, Munyque; Maubert, Bastien; Murano, Aniello; Perrussel, Laurent

doi:10.24963/ijcai.2022/61

Cited by 7 publications

(6 citation statements)

References 3 publications

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“…For example, to analyze and develop bidding strategies in sequential auctions or fair allocation of goods [11]. Further, it is interesting to study mechanism design: synthesize an arena so that the game has guarantees (e.g., [21]).…”

Section: Discussionmentioning

confidence: 99%

Reachability Poorman Discrete-Bidding Games

Avni,

Meggendorfer,

Sadhukhan

et al. 2023

Frontiers in Artificial Intelligence and Applications

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We consider bidding games, a class of two-player zero-sum graph games. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit bids, and the higher bidder moves the token, where we break bidding ties in favor of Player 1. Player 1 wins the game iff the token visits a designated target vertex. We consider, for the first time, poorman discrete-bidding in which the granularity of the bids is restricted and the higher bid is paid to the bank. Previous work either did not impose granularity restrictions or considered Richman bidding (bids are paid to the opponent). While the latter mechanisms are technically more accessible, the former is more appealing from a practical standpoint. Our study focuses on threshold budgets, which is the necessary and sufficient initial budget required for Player 1 to ensure winning against a given Player 2 budget. We first show existence of thresholds. In DAGs, we show that threshold budgets can be approximated with error bounds by thresholds under continuous-bidding and that they exhibit a periodic behavior. We identify closed-form solutions in special cases. We implement and experiment with an algorithm to find threshold budgets.

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Section: Discussionmentioning

confidence: 99%

Reachability Poorman Discrete-Bidding Games

Avni,

Meggendorfer,

Sadhukhan

et al. 2023

Frontiers in Artificial Intelligence and Applications

View full text Add to dashboard Cite

show abstract

“…For example, to analyze and develop bidding strategies in sequential auctions or fair allocation of goods [10]. Further, it is interesting to study mechanism design: synthesize an arena so that the game has guarantees (e.g., [20]).…”

Section: Discussionmentioning

confidence: 99%

Infinite-Duration All-Pay Bidding Games

Avni

Jecker

Zikelic³

2021

Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)

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In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In bidding games, however, the players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token: both players simultaneously submit bids and the higher bidder moves the token. The bidding mechanisms differ in their payment schemes. Bidding games were largely studied with variants of first-price bidding in which only the higher bidder pays his bid. We focus on all-pay bidding, where both players pay their bids. Finiteduration all-pay bidding games were studied and shown to be technically more challenging than their first-price counterparts. We study for the first time, infinite-duration all-pay bidding games. Our most interesting results are for mean-payoff objectives: we portray a complete picture for games played on strongly-connected graphs. We study both pure (deterministic) and mixed (probabilistic) strategies and completely characterize the optimal and almost-sure (with probability 1) payoffs the players can respectively guarantee. We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical properties of their firstprice counterparts; namely, an equivalence with random-turn games in which in each turn, the player who moves is selected according to a (biased) coin toss. The equivalences for allpay bidding are more intricate and unexpected than for firstprice bidding.

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“…However, more recent works in this area adopt multi-disciplinary methods such as automated mechanism design [30,27,37,3], which typically focus on the problem of constructing incentive-compatible mechanisms to optimise a particular objective such as social welfare. Other approaches in this area reduce mechanism design to a program synthesis problem [29] or a satisfiability problem for quantitative strategy logic formulae [25,28]. The notion of dynamic incentives has also been investigated in (multi-agent) learning settings [7,26,36,42,10].…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Incentive Engineering for Concurrent Games

Hyland

Gutiérrez

Wooldridge

2023

Electron. Proc. Theor. Comput. Sci.

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We consider the problem of incentivising desirable behaviours in multi-agent systems by way of taxation schemes. Our study employs the concurrent games model: in this model, each agent is primarily motivated to seek the satisfaction of a goal, expressed as a Linear Temporal Logic (LTL) formula; secondarily, agents seek to minimise costs, where costs are imposed based on the actions taken by agents in different states of the game. In this setting, we consider an external principal who can influence agents' preferences by imposing taxes (additional costs) on the actions chosen by agents in different states. The principal imposes taxation schemes to motivate agents to choose a course of action that will lead to the satisfaction of their goal, also expressed as an LTL formula. However, taxation schemes are limited in their ability to influence agents' preferences: an agent will always prefer to satisfy its goal rather than otherwise, no matter what the costs. The fundamental question that we study is whether the principal can impose a taxation scheme such that, in the resulting game, the principal's goal is satisfied in at least one or all runs of the game that could arise by agents choosing to follow game-theoretic equilibrium strategies. We consider two different types of taxation schemes: in a static scheme, the same tax is imposed on a state-action profile pair in all circumstances, while in a dynamic scheme, the principal can choose to vary taxes depending on the circumstances. We investigate the main game-theoretic properties of this model as well as the computational complexity of the relevant decision problems.

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Automated Synthesis of Mechanisms

Cited by 7 publications

References 3 publications

Reachability Poorman Discrete-Bidding Games

Reachability Poorman Discrete-Bidding Games

Infinite-Duration All-Pay Bidding Games

Incentive Engineering for Concurrent Games

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