Mechanism design has long been a cornerstone of economic theory, with traditional approaches relying on mathematical derivations. Recently, automated approaches, including differentiable economics with neural networks, have emerged for designing payments and allocations. While both analytical and automated methods have advanced the field, they each face significant weaknesses: mathematical derivations are not automated and often struggle to scale to complex problems, while automated and especially neural-network-based approaches suffer from limited interpretability. To address these challenges, we introduce a novel framework that reformulates mechanism design as a code generation task. Using large language models (LLMs), we generate heuristic mechanisms described in code and evolve them to optimize over some evaluation metrics while ensuring key design criteria (e.g., strategy-proofness) through a problem-specific fixing process. This fixing process ensures any mechanism violating the design criteria is adjusted to satisfy them, albeit with some trade-offs in performance metrics. These trade-offs are factored in during the LLM-based evolution process. The code generation capabilities of LLMs enable the discovery of novel and interpretable solutions, bridging the symbolic logic of mechanism design and the generative power of modern AI. Through rigorous experimentation, we demonstrate that LLM-generated mechanisms achieve competitive performance while offering greater interpretability compared to previous approaches. Notably, our framework can rediscover existing manually designed mechanisms and provide insights into neural-network based solutions through Programming-by-Example. These results highlight the potential of LLMs to not only automate but also enhance the transparency and scalability of mechanism design, ensuring safe deployment of the mechanisms in society.

Blockchains deploy Transaction Fee Mechanisms (TFMs) to determine which user transactions to include in blocks and determine their payments (i.e., transaction fees). Increasing demand and scarce block resources have led to high user transaction fees. As these blockchains are a public resource, it may be preferable to reduce these transaction fees. To this end, we introduce Transaction Fee Redistribution Mechanisms (TFRMs) -- redistributing VCG payments collected from such TFM as rebates to minimize transaction fees. Classic redistribution mechanisms (RMs) achieve this while ensuring Allocative Efficiency (AE) and User Incentive Compatibility (UIC). Our first result shows the non-triviality of applying RM in TFMs. More concretely, we prove that it is impossible to reduce transaction fees when (i) transactions that are not confirmed do not receive rebates and (ii) the miner can strategically manipulate the mechanism. Driven by this, we propose \emph{Robust} TFRM (\textsf{R-TFRM}): a mechanism that compromises on an honest miner's individual rationality to guarantee strictly positive rebates to the users. We then introduce \emph{robust} and \emph{rational} TFRM (\textsf{R}$^2$\textsf{-TFRM}) that uses trusted on-chain randomness that additionally guarantees miner's individual rationality (in expectation) and strictly positive rebates. Our results show that TFRMs provide a promising new direction for reducing transaction fees in public blockchains.

Redistribution mechanisms have been proposed for more efficient resource allocation but not for profit. We consider redistribution mechanism design for the first time in a setting where participants are connected and the resource owner is only aware of her neighbours. In this setting, to make the resource allocation more efficient, the resource owner has to inform the others who are not her neighbours, but her neighbours do not want more participants to compete with them. Hence, the goal is to design a redistribution mechanism such that participants are incentivized to invite more participants and the resource owner does not earn or lose much money from the allocation. We first show that existing redistribution mechanisms cannot be directly applied in the network setting to achieve the goal. Then we propose a novel network-based redistribution mechanism such that all participants in the network are invited, the allocation is more efficient and the resource owner has no deficit. Introduction The problem of resource allocation has recently caught the public imagination, where the resource owner has to decide the allocation of the item among a group of self-interested agents. Since the valuation differs from agents, it is a natural objective for the owner to pursue the efficiency of the allocation, i.e., allocating the item to the agent with the highest valuation. In many scenarios, the owner does not really aim at making profits but hopes the wealth maintained among the agents. For example, the government wants to build a library in a community that values it most; a charity distributes a donation to the recipient who needs it most; a hospital allocates doctors to rural areas where doctors are highly demanded. To find the agent with the highest valuation, one common alternative is to hold an auction (Krishna 2009) under some protocols such as the well-known Vickrey-Clarke- Groves (VCG) mechanism (Vickrey 1961; Clarke 1971; Groves 1973). However, the payments under VCG will all be delivered to the auctioneer, which againsts our nonprofit purpose.

We join the goals of two giant and related fields of research in group decision-making that have historically had little contact: fair division, and efficient mechanism design with monetary payments. To do this we adopt the standard mechanism design paradigm where utility is assumed to be quasilinear and thus transferable across agents. We generalize the traditional binary criteria of envy-freeness, proportionality, and efficiency (welfare) to measures of degree that range between 0 and 1. We demonstrate that in the canonical fair division settings under any allocatively-efficient mechanism the worst-case welfare rate is 0 and disproportionality rate is 1; in other words, the worst-case results are as bad as possible. This strongly motivates an average-case analysis. We then set as the goal identification of a mechanism that achieves high welfare, low envy, and low disproportionality in expectation across a spectrum of fair division settings. We establish that the VCG mechanism is not a satisfactory candidate, but the redistribution mechanism of [Bailey, 1997; Cavallo, 2006] is.

There are p heterogeneous objects to be assigned to n competing agents (n > p) each with unit demand. It is required to design a Groves mechanism for this assignment problem satisfying weak budget balance, individual rationality, and minimizing the budget imbalance. This calls for designing an appropriate rebate function. When the objects are identical, this problem has been solved which we refer as WCO mechanism. We measure the performance of such mechanisms by the redistribution index. We first prove an impossibility theorem which rules out linear rebate functions with non-zero redistribution index in heterogeneous object assignment. Motivated by this theorem, we explore two approaches to get around this impossibility. In the first approach, we show that linear rebate functions with non-zero redistribution index are possible when the valuations for the objects have a certain type of relationship and we design a mechanism with linear rebate function that is worst case optimal. In the second approach, we show that rebate functions with non-zero efficiency are possible if linearity is relaxed. We extend the rebate functions of the WCO mechanism to heterogeneous objects assignment and conjecture them to be worst case optimal.

In many multiagent settings, a decision must be made based on the preferences of multiple agents, and agents may lie about their preferences if this is to their benefit. In mechanism design, the goal is to design procedures (mechanisms) for making the decision that work in spite of such strategic behavior, usually by making untruthful behavior suboptimal. In automated mechanism design, the idea is to computationally search through the space of feasible mechanisms, rather than to design them analytically by hand. Unfortunately, the most straightforward approach to automated mechanism design does not scale to large instances, because it requires searching over a very large space of possible functions. In this paper, we describe an approach to automated mechanism design that is computationally feasible. Instead of optimizing over all feasible mechanisms, we carefully choose a parameterized subfamily of mechanisms. Then we optimize over mechanisms within this family, and analyze whether and to what extent the resulting mechanism is suboptimal outside the subfamily. We demonstrate the usefulness of our approach with two case studies.