**Bayesian learning in markets with common value**

**Rann Smorodinsky**

(Faculty of Industrial Engineering, Technion Israel Institute of Technology-Haifa)

**: Wednesday, January 24th at 3.00 pm**

When

When

**Where**: Seminar Room of the Department of Economics, Management and Statistics University of Milan-Bicocca, Piazza Ateneo Nuovo 1, Building U7, second floor, room 2104

Two firms produce substitute goods with unknown quality. At each stage the firms set prices and a consumer with private information and unit demand buys from one of the firms. Both firms and consumers see the entire history of prices and purchases. Will such markets aggregate information? Will the superior firm necessarily prevail? We adapt the classical social learning model by introducing strategic dynamic pricing. We provide necessary and sufficient conditions for learning. In contrast to previous results, learning

can occur when signals are bounded. This happens when signals exhibit the newly introduced vanishing likelihood property.

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**Permanent Itinerant Game Theory Seminars (P.I.G.S.)**

Bayesian Persuasion

Bayesian Persuasion

When is it possible for one person to persuade another to change her action? Persuasion plays a crucial role in many economic activities, e.g., courts, lobbying, financial disclosure and political campaigns. The general problem that will be discussed is how to persuade a rational agent by controlling her informational environment. We consider a symmetric information setting with an arbitrary state space and action space, an arbitrary prior, and arbitrary state-dependent preferences for both Sender and Receiver. Sender chooses an informative signal about the state of the world, Receiver observes a realization from this signal, and then she takes an action. Throughout the analysis, the Sender is prohibited from making transfers or affecting Receiver’s payoffs in any way. We focus on two questions:

(i) When does there exist a signal that strictly benefits Sender?

(ii) What is an optimal signal from Sender’s perspective?

This talk will discuss the work and results presented by Prof. Emir Kamenica (University of Chicago) at the 28th Jerusalem School in Economic Theory on Mechanism Design.

*Andrea Celli*

**Speaker:***: Tuesday, December 12th, 2017, 11:00 am*

**When***: PT1 Room (DEIB, building 20, ground floor), Politecnico di Milano, via Ponzio 34/5*

**Where****Online Learning techniques for optimization for internet advertising campaigns**

*Francesco Trovo'*

**Speaker:***: Tuesday, November 14th, 2017, 12:30 am*

**When***: Seminar Room of the Department of Electronics, Information and Bioengineering*

**Where****Equilibrium selection in games with complete information**

The selection of a unique equilibrium in games with multiple solutions has long been a critical issue in game theory, and the object of two research programs. The main and more successful attempted to provide an answer to this problem through the refinement of the equilibrium concept, which allowed to narrow down the number of solutions in many games, but only on certain circumstances to select a unique equilibrium. The alternative program sought to create a selection mechanism without relying on the refinement of an equilibrium. But the resulting methods are, in general, only possible to be applied on a small number of games, some are excessively complex, which prevents their empirical validation, and the selection criteria are not uncontested. We take these limitations into account and propose an equilibrium selection method to n-person non-cooperative games with complete information and a finite and non-empty set of pure strategy Nash equilibria, that uses both risk and payoff dominance as criteria to order players' preferences over the game solutions. We show that this method recurrently selects a unique solution, with exception of symmetric games, which represents the optimal equilibrium strategy choice for a player, conditional on the equilibrium preferences of the adversaries.

*Rui Miguel Constantino Da Silva*

**Speaker:***: Tuesday, November 7th, 2017, 11:00 am*

**When***: Seminar Room of the Department of Economics, Management and Statistics University of Milan-Bicocca*

**Where****Ranking object from preference relations on their subsets**

In many everyday situations it can happen that one wants to rank the elements of a group of people having the possibility to observe them collaborating in subgroups. In this work, we propose a general way to get this ranking over the elements of a group N, starting from an arbitrary preference relation over the subsets of N and taking into account the information provided by this ranking over the subsets. To discuss this issue, we use the standard approach to this type of problems, very common in the social choice framework: we single out some properties that a general solution should have, and we prove that these properties characterize a unique function. Given the very general type of problems that this model can represent, we believe that this is only a starting point for a more extended analysis. In particular, it is clear that different contexts can suggest different properties that could identify other procedures.

*Giulia Bernardi*

**Speaker:***: Tuesday, October 3th, 2017, 1 pm*

**When***: 3rd floor, Seminar Room of the Department of Mathematics*

**Where**Building 14, Politecnico di Milano

**Power indices for games with abstention**

Simple games are usually used as a model for binary voting situations. However, in some voting systems players have a third intermediate and separate option: to abstain. These more general voting situations are modelled by (3,2) simple games or ternary voting games.

In this work we study solution concepts for (3,2) simple games analogous to those defined for simple games, such as the Banzhaf or the Shapley-Shubik indices. We mainly focus on axioms and bargaining procedures associated to these indices.

*Giulia Bernardi*

**Speaker:***: Thursday, April 6th, 2017, 1.30 pm*

**When***: Seminar Room of the Department of Economics, Management and Statistics*

**Where**University of Milan-Bicocca, Piazza Ateneo Nuovo 1,

Building U7, second floor, room 2104

**Investment Cost Sharing for Rural Electrification**

This study is motivated by the Sustainable Development Goal number 7: “Ensure access to affordable, reliable, sustainable and modern energy for all”. To support rural electrification policies, we propose a model to allocate investment costs of a micro-grid among its users.

Starting from the LP-relaxation of a facility location problem, we show how introducing capacity constraints force us to use rationing rules to share the costs.

We propose a case study based on real data from an Indian rural village, where a group of farmers – 15 players – may want to share electric generators to pump water for irrigation purpose.

*Giorgio Bonamini*

**Speaker:***: Thursday, March 23, 2017, 1.30 pm*

**When***: Seminar Room (3rd floor) of the Department of Mathematics, Building 14, Politecnico di Milano, Via Bonardi 9, Milano*

**Where**

**Computing Solutions in**

**Leadership Games**

In recent years, leader-follower (or Stackelberg) games have attracted a growing interest in Artificial Intelligence. In the two-player case, these games describe situations where one player (leader) commits to a strategy and the other player (follower) first observes the leader’s commitment and, then, decides how to play. This is the case of security games, where a defender (leader) is tasked to allocate scarce resources to protect valuable targets from an attacker (follower). In this talk, we first analyse the single-follower scenario, differentiating between two cases: the optimistic one, where the follower breaks ties to maximize the leader’s utility, and the pessimistic case, where the follower acts so as to minimize it. Then, we switch to the multi-follower setting, assuming the followers play noncooperatively and simultaneously, thus reaching a Nash equilibrium. We focus on the pessimistic case with followers restricted to play pure strategies, showing that the problem is hard and presenting an algorithm to solve it.

*Alberto Marchesi*

**Speaker:***: March 2, 2017, 1.30 pm*

**When***: Sala Seminari Alessandra Alario, Department of Electronics, Information and Bioengineering Politecnico di Milano*

**Where**Via Ponzio 34/5, Milano

**Adversarial Team Games**

Adversarial team games model strategic settings in which a team of rational agents sharing the same goals plays against an adversary. These games describe a wide array of real-world scenarios such as, in the security setting, those where multiple agents share the common objective of defending an environment against a malicious attacker. In this talk, we first describe the solution concepts related to the possible coordination capabilities of the team. In particular, we introduce the Team-maxmin equilibrium as a means to prescribe the optimal strategy to the team when correlation is not possible. We evaluate the inefficiency bounds of such an equilibrium w.r.t. Nash equilibria and the maxmin equilibrium achievable when teammates can play over correlated strategies. Then, we present some algorithms able to cope with real-world game instances. In the last part of the talk we will focus on current research being done on further extensions of these models.

*Andrea Celli*

**Speaker:***: February 16, 2017, 1.30 pm*

**When***: Seminar Room of the Department of Economics, Management and Statistics*

**Where**University of Milan-Bicocca, Piazza Ateneo Nuovo 1,

Building U7, second floor, room 2104

**

**Learning for Pricing**

As is customary in e-commerce scenarios, the design of effective algorithms for learning prices is a problem of extraordinary importance in settings in which the demand curve is not a priori known and its estimation takes a long time. Adopting effective pricing algorithms potentially allows companies to increase dramatically their profits. Since economics scenarios are characterized by lack of information (uncertainty about the user preferences), non-stationarity (due to both competitors price obscillations and seasonal effects) and huge catalog of products, it is necessary to develop automatic techniques to handle the burden of the optimization procedure.

In this talk, we formulate the pricing optimization problem as a contextual Multi–Armed Bandit (MAB) problem and we present the design of novel MAB algorithms able to exploit the characteristics of the considered pricing problem. In the first part, we consider common assumptions about the pricing setting (i.e., monotonicity of the converasion rate, unimodality of the expected profit function and constraints on cost budget) to enhance the performance of the state of the art MAB algorithms. After that, we exploit the logged information available to past transactions to partition the decision space, allowing to handle the huge catalog of products.

*Stefano Paladino*

**Speaker:***: February 02, 2017, 1.30 pm*

**When***: Seminar Room of the Department of Economics, Management and Statistics*

**Where**University of Milan-Bicocca, Piazza Ateneo Nuovo 1,

Building U7, second floor, room 2104

**Games for Security**

Physical security is one of the most important challenges of our times. Due to the terrible events happened in the last decades, new techniques and methods are being developed to face new threats and dangers. On the other side, security means also saving lives, e.g. detecting desperate migrants that are moving across the Mediterranean Sea and rescuing them.

Game theory is a fundamental tool in these settings, allowing us to model situations with criminals, called Attackers, and guards, denoted as Defenders, as strategic form games in which the behaviors of such actors can be analyzed. This approach is of high prominence in practice, allowing for remarkable improvements of the levels of protection and security.

*Giuseppe De Nittis*

**Speaker:***: January 19, 2017, 1.30 pm*

**When***: Sala Seminari, Department of Electronics, Information and Bioengineering Politecnico di Milano*

**Where**Via Ponzio 34/5, Milano