Mechanism Design Powered by Social Interactions
aa r X i v : . [ c s . G T ] F e b Mechanism Design Powered by Social Interactions
Blue Sky Ideas Track
Dengji Zhao
ShanghaiTech UniversityShanghai, [email protected]
ABSTRACT
Mechanism design has traditionally assumed that the set of partici-pants are fixed and known to the mechanism (the market owner) inadvance. However, in practice, the market owner can only directlyreach a small number of participants (her neighbours). Hence theowner often needs costly promotions to recruit more participantsin order to get desirable outcomes such as social welfare or rev-enue maximization. In this paper, we propose to incentivize exist-ing participants to invite their neighbours to attract more partici-pants. However, they would not invite each other if they are com-petitors. We discuss how to utilize the conflict of interest betweenthe participants to incentivize them to invite each other to formlarger markets. We will highlight the early solutions and open thefloor for discussing the fundamental open questions in the settingsof auctions, coalitional games, matching and voting.
KEYWORDS
Mechanism Design; Social Networks; Diffusion Incentives; Auc-tions; Coalitional Games; Matching; Social Choice
ACM Reference Format:
Dengji Zhao. 2021. Mechanism Design Powered by Social Interactions: BlueSky Ideas Track. In
Proc. of the 20th International Conference on AutonomousAgents and Multiagent Systems (AAMAS 2021), Online, May 3–7, 2021 , IFAA-MAS, 5 pages.
Mechanism Design studies how to implement desirable social choicefunctions in a strategic environment where all participants act ra-tionally in game theoretical sense. Auction as one of the key out-puts of mechanism design has been widely used in different mar-kets for a long history (dates back to 17th century) [41]. Vickreyauction is the seminal work of Vickery [44] which inspired manyauction theories such as Vickrey-Clarke-Groves (VCG) auction [10,16], Gibbard-Satterthwaite theorem [15, 36], Myerson’s revenue-maximizing auction [26] and Myerson-Satterthwaite theorem [27].In addition to the rich theoretical results, in the beginning of 21stcentury, IT service providers like Google started to apply a modi-fication of Vickrey auction, called generalized second-price (GSP)auction, to allocate ad impressions [12]. Although GSP does nothave the desirable property called truthfulness as Vickrey auctiondoes, it has been a golden mechanism for online advertising.As the technology of smart devices keeps pushing the bound-aries in the last decade, more and more IT services have been moved
Proc. of the 20th International Conference on Autonomous Agents and Multiagent Sys-tems (AAMAS 2021), U. Endriss, A. Nowé, F. Dignum, A. Lomuscio (eds.), May 3–7, 2021,Online to smart devices such as online shopping and online games. Manysocial networking applications like TikTok are purely built on smartdevices. This also pushed the online advertising market shiftingfrom traditional PC-based channels to smart-device-based chan-nels [1]. More importantly, we see many new forms of mechanismsfor online advertising/shopping utilising users’ connections/interactionson social networks [25, 30].As the Internet is moving from traditional PC-network to socialnetworks and in the near future to Internet of Things, we havemore personal information from the Internet than before. For ex-ample, from a smart phone, with its owner’s permission, we canget the owner’s social connections, preferences, locations, photos,reviews, shopping history and etc.. This opens up a huge new spacefor market design which, of course, is not just for advertising.In a mechanism design setting, we model all the informationthat a mechanism needs to elicit from the participants as theirtypes. In the literature, the types are typically cardinal or ordinalpreferences on outcomes. Moreover, the participants are mostly as-sumed to be independent. However, in the modern economy under-pinned by social networks, people are well-connected. They canquickly gather together online to share resources, distribute tasksor make decisions, even though they are not physically together.Hence, it is essential to explicitly model and utilize their connec-tions in the corresponding market design stage.In this paper, we propose to utilize people’s social connectionsto invite each other to build larger markets, which enables the mar-ket to achieve better outcomes. However, people would not inviteeach other when there is a competition among them, say, in a lim-ited resource allocation. We discuss how to resolve the conflict ofinterest among the participants to incentivize them to invite eachother, especially, in the settings of resource allocation, task alloca-tion, matching and voting.In the four mentioned settings, it is easy to see both the benefitsand challenges of attracting more participants. • In resource allocation (auctions), a larger market will dis-cover more participants’ valuations/demand and increasesocial welfare or the seller’s revenue. The challenge is toask participants to invite other participants to compete forthe same resources. • In task allocation (coalitional games), a larger group of par-ticipants creates larger coalitions (better outcomes/utilities).For example, in a research project, it is always good to addsomeone with different skills to the team. However, the newlyadded member might also have some skills which the teamalready has, which creates a competition for the reward shar-ing among the participants.
In matching, a larger group of participants makes more sat-isfiable matchings, e.g., larger exchange cycles. The sameas in the resource allocation, newly invited participant maycompete with their inviters for the match. • In voting, when we have more voters to vote, it will not onlyincrease the turnout rate but also make the voting resultsharder to manipulate. The challenge is that a voter wouldnot invite someone with different preferences.In the rest of the paper, we will model the challenges and discusspossible techniques to incentivize participants to invite their com-petitors in the four settings. Although they share a similar chal-lenge, the methods to tackle it are very different. Other mechanismdesign settings such as facility allocation and public goods are notdiscussed here, but they all can be studied under this framework.
Here we describe a general model of mechanism design on socialnetworks. We consider a game with 𝑛 players and they are con-nected via their social connections to form a connected social net-work. Let 𝑁 be the set of all players. Each player 𝑖 ∈ 𝑁 has a type 𝜃 𝑖 = ( 𝑟 𝑖 , 𝑝 𝑖 ) , where 𝑟 𝑖 ⊂ 𝑁 is 𝑖 ’s neighbours (with whom 𝑖 candirectly communicate and 𝑖 does not know the others 𝑁 \ 𝑟 𝑖 ) inthe network and 𝑝 𝑖 is 𝑖 ’s other private information defined for thespecific game. For example, in a single item auction, 𝑝 𝑖 is 𝑖 ’s valua-tion for the item. In a house allocation, 𝑝 𝑖 can be 𝑖 ’s preference onall exchangeable houses. In all the different settings, one commonparameter of 𝑖 ’s type is her neighbours 𝑟 𝑖 .To execute a mechanism in the model, we need a mechanism/marketowner. In this model, the owner can be a special player in the net-work. For example, a seller for an item or a sponsor for a set oftasks. Let 𝜔 ∈ 𝑁 be the mechanism owner. It is evident that with-out attracting more participants, 𝜔 can only run the mechanismamong her neighbours 𝑟 𝜔 . In addition to the traditional goals, thenew goal of the mechanism design here is to incentivize 𝑟 𝜔 to in-vite their neighbours to join the mechanism and the newly invitedplayers would further do the same. Eventually, everyone from thenetwork is invited and the owner can run the mechanism amongall of them.In the traditional mechanism design settings, 𝑖 ’s type is just 𝑝 𝑖 .One important property called incentive compatibility (a.k.a. truth-fulness) is defined as "if a mechanism is incentive compatible, thenfor all 𝑖 ∈ 𝑁 \ { 𝜔 } , reporting 𝑝 𝑖 truthfully to the mechanism isa dominant strategy". In our model, the type space is enlargedand we need to extend the definition of incentive compatibilityto cover the action of inviting their neighbours. To model the in-vitation action mathematically, we also ask them to report theirneighbour sets to the mechanism, which does not affect the actualimplementation in practice. Then the new definition becomes "foreach 𝑖 ∈ 𝑁 \ { 𝜔 } , reporting both 𝑝 𝑖 and 𝑟 𝑖 truthfully is a dominantstrategy".In the traditional settings, when 𝑖 misreports 𝑝 𝑖 , it will not affectthe other players’ participation/reports. However, in our model, if 𝑖 misreports 𝑟 𝑖 (i.e., 𝑖 does not invite all her neighbours), some play-ers may not be able to participate any more. For example, if a player 𝑗 can only be invited by 𝑖 and if 𝑖 does not invite 𝑗 , then 𝑗 and all theother players connected to 𝑗 will not be able to join the mechanism. Therefore, misreporting in this model will affect the participationof the others, which is a key challenge in the design. Resource allocation has been the mostly studied setting for mech-anism design. Auctions such as VCG mechanism have been de-veloped for resource allocation to achieve the desirable proper-ties such as truthfulness, efficiency, and individual rationality. An-other important property of resource allocation is maximizing theseller’s revenue. It has been shown that VCG mechanism cannotmaximize the revenue at the same time and especially, for com-binatorial settings, the revenue of the seller may decrease whenthere are more buyers [29, 32]. This also explains why under VCG,a buyer can create false ids to pretend to be multiple buyers topay less for the same set of items [45]. To further maximize theseller’s revenue, Myerson [26] proposed the very first mechanismto achieve the optimal revenue for selling a single item. The ideais to add a reserve price on top of the VCG and the reserve pricerequires buyers’ valuation distributions. However, in practice, themost efficient way to increase the revenue is to seek more buyers tocompete for the item. This is also justified in theory by Bulow and Klemperer [6]and they showed that in the single-item setting, the optimal rev-enue with 𝑛 buyers is not more than the revenue of VCG with 𝑛 + 𝑝 𝑖 in this setting isa valuation function for all bundles of the items. The goal for theseller is to design a mechanism such that participants are incen-tivized to both report their valuation function truthfully and in-vite all their neighbours to join the sale. Also the seller’s revenueshould not be smaller than directly selling the items to her neigh-bours only (an incentive for the seller to apply the mechanism).Given the above setting, some novel mechanisms have recentlybeen proposed for single-item settings and multiple identical itemssettings [23, 51]. The intuition behind their mechanisms is that abuyer can potentially benefit from inviting her neighbours. If auyer does not invite anyone and wins the item, he will get a util-ity say 𝑥 . If the buyer invited all her neighbours, then the buyermay lose the item, but the mechanism guarantees that the buyer’snew utility 𝑦 is not less than 𝑥 . This could be understood as thatthe buyer first buys the item and then resells it to her neighbourswith a higher price. If the reselling price is not higher than the cur-rent buyer’s valuation, then the buyer will keep the item. This alsoexplains that why their mechanisms are not efficient (not maximiz-ing social welfare). One important property of their mechanisms isthat the seller’s revenue is guaranteed to be non-decreasing, whichmeans that the seller is incentivized to use the diffusion mecha-nisms to increase her revenue.To get complete efficiency, VCG can be extended to incentivizebuyers to invite each other, but the revenue of the seller will benegative [23]. It is not hard to prove that under the network set-ting, it is impossible to achieve truthfulness, individual rationalityand efficiency together with non-negative revenue for the seller(which can be proved by converting a simple model (where a sellerconnects to buyer A and buyer A further connects to buyer B) intoa bilateral trading case [21, 47]). One interesting open question ishow much efficiency we can approximate given that the seller’srevenue is non-negative. We believe that this largely depends onthe structure of the network and the buyers’ valuation distribu-tions. The mechanisms cited above, except for the VCG, has noguarantee in terms of approximating efficiency.Another more challenging open question is to design similarmechanisms for multiple heterogeneous items settings. It has beenshown that the problem becomes extremely difficult when we movejust one step forward from single-item to multiple homogeneousitems cases [20, 51]. The difficulty comes from the fact that the al-location and price of one participant can be easily influenced byits invitees and siblings [51]. In order to get the property of truth-fulness, we need to maximize everyone’s utility, which leads toa super complex multiagent optimization problem. One possiblebreakthrough is to restrict the action space of the participants tosimplify the optimization. Also there is a hierarchy problem fol-lowing their invitations, where an inviter has a higher priority inthe optimization than her invitees. Task allocation is another important field of mechanism design.One setting is where there is one task to be finished and there area number of workers who can perform the task with different (pri-vately known) costs, and the goal is to find a suitable worker [40].This setting can be transferred to the resource allocation setting(the task can be treated as a resource). What we consider here arecooperative games such as coalitional games and crowdsrourcinggames. In a coalitional game, players can form groups to achievedifferent rewards and the goal is to design a reward distributionmechanism to incentivize them to work together as one group(a.k.a. grand coalition) [8]. In a crowdsourcing game, we have aset of tasks to do and the goal is to find the best set of workersto perform them such as tasks on Amazon Mechanical Turk andGoogle Image Labeler [11, 17]. Different from the resource allo-cation settings, we have both collaboration and competition here.The collaboration comes from the fact they need to work together to accomplish the tasks and the competition is due to the rewarddistribution.In order to incentivize the players to collaborate in a coalitionalgame, the literature has focused on designing proper reward dis-tribution mechanisms [8]. Shapley value is one of the well-knowndistribution mechanisms satisfying many desirable properties [39].Core is another important property which says a distribution is acore if no subset of players can deviate from the grand coalitionto receive better rewards [37]. Shapley value is computable for allcoalitional games, but core may not exist for all the games. Sincea larger group of players work together can achieve more, we con-sider how to incentivize players to invite others (via their socialconnections) to join the game, which is widely applicable in prac-tice. This is not well-considered in the literature and cannot besolved with the existing solutions.Consider a simple example where initially only player 𝑃 is inthe game and 𝑃 can achieve a utility 𝑥 alone. If 𝑃 has a neigh-bour 𝑃 whose ability is the same as 𝑃 , i.e., they together cannotachieve more than 𝑥 . If we apply Shapley value, 𝑃 receives 𝑥 with-out inviting 𝑃 , but it is reduced to 𝑥 / 𝑃 . Thus, 𝑃 isnot incentivized to invite 𝑃 if the reward is distributed by Shapleyvalue. Actually, in this simple example, the reward distributed to 𝑃 should be at least 𝑥 in order to incentivize 𝑃 to invite others.Therefore, our goal is to design new reward distribution mecha-nisms to incentivize them to not only work together, but also invitemore players to cooperate together to receive better rewards. Weassume that the players are connected to form a network and ini-tially only a subset of them are in the game. The challenge is thatwe cannot treat inviters and invitees the same and in principle in-viters have higher priorities/weights than invitees. The question ishow to use this priority to define the reward distribution.Zhang et al. [46] studied a data acquisition setting by modify-ing Shapley value such that the join of invitees may only increasethe Shapley value that the inviters can get before the invitation. Bydoing so, they group all players by layers, the first layer containsall the initial players, the second layer contains all the players di-rectly invited by the first layer and so on. If we treat each layeras one group, then the reward distributed to the 𝑘 -th layer is themarginal contribution when the 𝑘 -th layer join after the first 𝑘 − In both resource and task allocation, we often use utility transfer(monetary payment) to achieve the design goals. However, in somesettings like matching, monetary payment is not an option. Match-ing is a well-studied field consisting of problems like house allo-cation, stable marriage problem and kidney exchange [18, 33, 34,42]. In a matching setting, players have mainly ordinal preferencesamong different matchings, e.g. a player prefers house 𝑎 to house 𝑏 but does not have an exact value for each house. Also in kidney ex-change, a donor cannot charge the patient who received the dona-tion. Without the tool of utility transfer, the literature has focusedon making optimal or stable matching such as the top trading cy-cle algorithm for house allocation and the Gale-Shapley algorithmfor stable marriage problem [14, 38].We further study the matching problem from the perspectiveof attracting more participants. For example, in a house allocationor stable marriage problem, more participants will create betterexchanges and make participants more satisfied. Again, in kidneyexchange, if we have more donors and patients, we will be able toform more exchanges and benefit more patients [35, 42].The challenge we tackle here is how to incentivize existing par-ticipants to invite others who are not in the matching game yet.Existing solutions cannot solve this. Consider the top trading cyclealgorithm for house exchange, if a participant 𝑃 invited anotherparticipant 𝑃 , 𝑃 may compete with 𝑃 for the same house. For theGale-Shapley algorithm in a stable marriage problem, if a man 𝑀 invited another man 𝑀 who has the same preference as 𝑀 does,then 𝑀 will compete with 𝑀 for the same women. Even if 𝑀 in-vites a woman 𝑊 , 𝑊 could again invite 𝑀 to compete with 𝑀 .Thus, both men and women would not invite others by default.Therefore, we need to investigate new matching mechanismsto incentivize existing participants to invite new participants. Sim-ilar to the resource and task allocation, the key is that an inviters’match should not be sacrificed by their invitees. In traditional set-tings, we allow participants to have a full preference among allparticipants without any constraints, but in the network setting,we need to add constraints on their preferences in order to incen-tivize them to invite each other. For the example mentioned above, if 𝑃 competes with 𝑃 for the same house, assume their preferredhouse is with 𝑃 and 𝑃 does not know 𝑃 , even if 𝑃 prefers 𝑃 ’shouse to 𝑃 ’s house, we cannot allow 𝑃 and 𝑃 exchange directly(otherwise, 𝑃 would not invite 𝑃 to the game). The challenge hereis how to interpret this kind of constraint in the matching process.Zheng et al. [52] proved that to incentivize participants to inviteeach other, we cannot further have the traditional optimality. Thus,the existing matching mechanisms cannot work in the new setting. Voting is another important field in mechanism design where mon-etary transfer is not possible [5, 28]. Due to the development of so-cial networks, more and more pools/votings are conducted onlineby inviting participants on social media [3, 4, 13]. On one hand, wehope more participants can join a voting to make the results reflectthe opinions of the majority. On the other hand, the invited partic-ipants are often the candidates’ friends, which makes the resultsunfair/biased to some extent. To combat this challenge, we proposeto design new voting rules such that more participants are invitedby the existing participants even if they have different preferences.More importantly, we hope the voting results are not far from theresults we can get when they all can participate without invitation.Intuitively, if it is a voting for choosing one winner, assume thatthe winner is 𝑎 when all participants vote under a classical votingrule. Then, under the new voting rule, except for attracting morevoters, we also hope that the final voting result is not far from 𝑎 . Ifsuch mechanism exists, we can always start a voting with a smallnumber of voters in the community. The initial voters will spreadthe voting to their network and eventually all the voters in the com-munity will be invited and the results still reflect the preferencesof the majority.The challenge here is that a voter preferring outcome 𝑎 to 𝑏 doesnot have incentives to invite voters preferring 𝑏 to 𝑎 . This alsoexplains why online votings are eventually a competition of thenumber of friends they have invited between the candidates. Weneed to change this by incentivizing the voters to invite all votersthey know, even though they may have different preferences. Tothe best of our knowledge, no solution has been found for this.One possible way to tackle the bias in online voting is liquiddemocracy (proxy voting). Voting via social network can easily re-alize the delegation process. Besides, those who are indifferent cantransfer their voting right to knowledgeable people [2, 19]. How-ever, existing mechanisms satisfying the delegation process cannotachieve a better outcome than each voter votes directly [7]. We have highlighted a new mechanism design challenge under thesocial network environment where each player is connected withsome players (her neighbours) and the player does not know theothers on the network. The design goal is to incentivize the play-ers who are already in the game to further invite their neighboursto join the game, even though they are competing for the sameresources, tasks or matches. We have emphasized four domains:auctions, coalitional games, matching and voting. They all haveifferent goals and face different challenges, but in terms of incen-tivizing the players to invite each other, they share the same prin-ciple that invitees cannot sacrifice their inviters’ utilities. We haveseen some progress in this direction on auctions and coalitionalgames, but there are still many fundamental open questions to beanswered. Of course, the diffusion study is not limited to the fourdomains. Any mechanism design settings where there is a need toattract more players can be studied under this framework.
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