Funded by the European Union (ERC, SUEE, n.759424). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.”

ERC Starting Grant, n. 759424: Extended Summary

This research project consists of two sets of projects: (i) Strategic Uncertainty in Economic Environments (SUEE), and (ii) Online Advertisement Auctions (OAA). 

Part 1-SUEE:

Equilibrium models in economics assume that agents know how others behave (their strategies). Hence, whereas agents may be uncertain about fundamental parameters of the environment, they face no “strategic uncertainty” (SU). Yet, a large industry has flourished that sells information not only about consumers’ characteristics (e.g. income, health, etc.), but also about how consumers’ behaviour (e.g., purchases, bidding histories, etc.) is correlated with such characteristics. The latter kind of information can be thought of precisely as information about players’ strategies in a game (i.e., how agents’ actions vary with their type), and hence it only has value if there is strategic uncertainty. The very existence of these markets therefore testifies to the economic importance of understanding SU.

Within classical game theory, solution concepts such as rationalizability (Bernheim (1984) and Pearce (1984)) have been developed to model SU. The experimental literature on initial responses has also led to various models of strategic thinking (level-k (Nagel, 1995), Cognitive Hierarchy (Camerer, Ho and Chong, 2004), Noisy Introspection, (Goeree and Holt, 2004), etc.) While important within game theory, these non-equilibrium approaches have not always had the diffusion they deserve in the broader economics literature. This part of the proposal aims at favouring a better integration of SU with classical economics, from both a behavioural and a classical perspective.

Part 1.1 approaches the problem of SU from a behavioural viewpoint, exploring the foundations and the implications of modelling the reasoning process of boundedly rational agents as a cost-benefit analysis, in which cognitive costs are weighed against the agent’s assessment of the benefits of reasoning. 

The paper “Cost-Benefit Analysis in Reasoning” (Alaoui and Penta, 2022, Journal of Political Economy) analyses the foundations of this modelling choice, by identifying the primitive properties of reasoning that must hold for the decision to stop thinking to be represented by a cost-benefit analysis. We also identify additional properties that give more structure to the value-of-reasoning function, and show that the cost-benefit model applies to a variety of settings, including R&D applications in Industrial Organization, models of Response Time in individual decision-making, and models of Strategic Reasoning. The results in this paper also served as further input for two other articles. 

In “Reasoning about Others’ Reasoning’’ (Alaoui, Janezic and Penta, 2020, Journal of Economic Theory), we study to what extent individuals’ behaviour in games is driven by their reasoning about others’ cognitive capacities, as opposed to their own cognitive limitations. The paper develops two methods to disentangle these effects in the lab (namely, the ‘replacement’ and ‘tutorial’ methods). The experimental results show that a significant fraction of subjects do take into account others’ incentives to reason, and lend further support to the cost-benefit approach developed in the first paper, and by our earlier research on “Endogenous Depth of Reasoning” (Alaoui and Penta, 2016, Review of Economic Studies). 

In “Coordination and Sophistication” (Alaoui, Janezic and Penta, 2023, R&R at Journal of the European Economic Association), we show that a large class of reasoning processes, the cost-benefit approach delivers sharp results about a long-lasting question in game theory. That is, whether equilibrium coordination can emerge, in the absence of focal points, as the outcome of purely introspective reasoning. We show that this is the case if players perceive heterogeneity in their cognitive abilities, rather than homogeneity. In addition, and perhaps contrary to common perception, it is not necessarily the case that being of higher cognitive sophistication is beneficial to the agent: in some coordination games, the opposite is true. An experimental test of the theory shows that subjects’ behaviour in the laboratory is consistent with these theoretical predictions, lending further support to the cost-benefit approach to reasoning. 

Altogether, part 1.1 of the project is important from several viewpoints: (i) from a foundational and methodological viewpoint, we identified to what extent standard concepts for economics (namely, cost-benefit and incentives) can be adequate to model reasoning processes; (ii) from a positive viewpoint, we showed that individuals do take others’ incentives to reason into account, thereby shedding light on subtle and little understood aspects of individuals’ strategic reasoning; (iii) the results on coordination and sophistication address a long-lasting question in game theory (i.e., eductive coordination), and shed light on the much broader theme concerning the relationship between measures of cognitive abilities, strategic sophistication, intelligence and economic performance.

Part 1.2 approaches the problem of Strategic Uncertainty from a classical viewpoint, i.e. under the standard assumptions for fully rational and ‘infinitely sophisticated’ (namely, Rationality and Common Belief in Rationality (RCBR)). 

The papers “Efficient Implementation via Transfers: Uniqueness and Sensitivity in Symmetric Environments” (Ollár and Penta, 2022, AEA p&p) and “A Network Solution to Robust Implementation: the case of Identical but Unknown Distributions” (Ollár and Penta, 2023, Review of Economic Studies), identify the conditions under which, with minimal information about agents’ beliefs, a scheme of monetary incentives can be designed to extract agents’ private information, so as to induce socially desirable goals while at the same time eliminating Strategic Uncertainty. These results address several long-lasting open problems in mechanism design, that is how to rule out the existence of multiple equilibria and undesirable solutions, without relying on unrealistically complicated mechanisms or strong assumptions on agents beliefs. From a methodological viewpoint, these papers uncovered a formal connection between the problem of designing monetary transfers to elicit agents’ information, with a problem of optimal design of a Network of strategic externalities. The study of implementation problems, albeit from a different perspective, is further pursued in the paper “Safe Implementation” (Gavan and Penta, 2023, R&R at Theoretical Economics), which introduces a new framework that allows to accommodate, within classical implementation theory, a variety of extra desiderata that include robustness concerns with respect to mistakes in play, model misspecification, behavioral considerations, state-dependent feasibility restrictions, limited commitment, and others.

In “Rationalizability, Observability and Common Knowledge” (Penta and Zuazo-Garin, 2022, Review of Economic Studies) we provide a systematic analysis of Strategic Uncertainty when players face higher-order uncertainty over the observability of their moves. Among other things, our general results have the following implications: (1) in a large class of conflict and common interest games (namely, zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium), the efficient equilibrium emerges, generically, as the only outcome consistent with players’ reasoning; (2) in a class of games which also includes other well-known families of coordination games, equilibrium coordination on the equilibrium most favourable to the first-mover ensues generically, regardless of whether his action is actually observable. Result (1) extends, from a classical perspective, the investigation from Part 1.1 on how equilibrium coordination can be achieved on the grounds of purely introspective reasoning (eductive coordination), identifying a new source for the resolution of Strategic Uncertainty (namely, uncertainty over the observability of actions). Result (2) contrasts with the received game theoretic wisdom that observability, not timing, is key to ensure a first-mover advantage. This result shows that this classical insight is fragile, and in fact overturned, when one considers even arbitrarily small departures from the standard assumptions on the observability of actions. Finally, the result is consistent with a wide body of previously unaccounted for experimental evidence.

Altogether, part 1.2 of the project produced several methodological innovations, which changed the received wisdom on fundamental game-theoretic insights about: (i) the sources of equilibrium coordination under Strategic Uncertainty; (ii) the determinants of the strategic advantage; (iii) the possibility to achieve socially desirable outcomes via the design of simple monetary transfers under strategic uncertainty. Furthermore, it bridged the literature on implementation and Networks, to gain insights about the sources of uniqueness of equilibrium in both settings. The results are thus useful also to address questions of optimal network design.

Part 2-OAA:

Search engines like Bing-Yahoo! and Google and social media like Facebook sell advertisement space on their pages using auctions. This is a huge market, with an annual growth of 10% and a total value of 50 billion dollars in 2013 in the US alone. A recent trend in this market is that an increasing fraction of advertisers delegate their bids to specialised Digital Marketing Agencies (DMA), which often bid in the same auctions on behalf of different advertisers and may thus manipulate the auctions and lower the bids of their clients. This project consists of an analysis of the impact of DMAs on the performance of both the GSP auction (used by Google and Yahoo!) and the VCG auction (used by Facebook). The analysis aims to identify the optimal strategies for the DMAs to coordinate their bids, their effects on the revenues and efficiency of the auction formats, and to generate insights on possible modifications to the auction mechanisms. 

In the paper “Marketing Agencies and Collusive Bidding in Online Ad Auctions” (Decarolis, Goldmanis, and Penta, 2020, Management Science), we provide a theoretical analysis of these questions. We show how collusive bidding can emerge from bid delegation to a common marketing agency and how this can undermine the revenues and allocative efficiency of both the generalised second-price auction (GSP, used by Google, Microsoft Bing, and Yahoo!) and the Vickrey-Clarke-Groves (VCG) mechanism (used by Facebook). We find that despite its well-known susceptibility to collusion, the VCG mechanism outperforms the GSP auction in terms of both revenues and efficiency. We argue that the fragility of these mechanisms to the presence of DMAs is bound to have an important impact on this industry.

The paper “Bid Coordination in Sponsored Search Auctions: Detection Methodology and Empirical Analysis” (Decarolis, Goldmanis, Shakhgildyan, and Penta, 2023, Journal of Industrial Economics), builds on this earlier theoretical work, to provide an empirical methodology to detect `coordinated’ bidding, as well as an empirical strategy to estimate a bound on the search engine’s revenue losses due to coordinated bidding, compared to a counterfactual benchmark in which all bidders bid competitively. We find that coordinated bidding in the data is detected in 55% of the cases where bids are delegated to an agency, and the associated upper bound on revenue losses for the search engine ranges between 5.3 and 10.4 percent.

In “Markets Effects of Sponsored Search Auctions“ (Motta and Penta, 2022, BSE working paper), We investigate the market effects of ad auctions on brand searches. We find that, compared to a benchmark where only organic search exists, brand search ad auctions have detrimental effects on welfare: (i) the sponsored link crowds out the rival’s organic link, thus reducing competition and choice, and leading to price increases; (ii) the payment of the rival’s bid (may) raise marginal cost, also contributing to raise market prices. Under extreme asymmetry (e.g., if there is an incumbent and an unknown new entrant), we do find that brand search auctions might be beneficial, but only if the search engine does not list the entrant’s link in organic search, and the share of the sophisticated consumers that compare all prices is large enough.

Overall, Part 2 of this project has shed some light on an important recent trend in an economically very important market. The theoretical and empirical results both suggest that the increased diffusion of DMAs can significantly erode the revenues of the main digital platforms. This suggests that further innovations should be expected in these markets, as the platforms will have the incentives to react to these forces, and adjust their auction mechanisms. The impact on consumers’ welfare is ambiguous, and depends importantly on several details of the environment. This line of research spells out some of such determinants in this important class of markets, and advances our understanding of the societal welfare in these markets.

The results of these research projects, combined, have been presented in tens of seminars and conferences throughout the world, including several keynotes and plenary or semi-plenary talks. The project has also funded the organisation of seven workshops, and several research visits.