London School of Economics and Political ScienceWednesdayThursday July 1112, 2018Organizer: Bernhard von StengelSpeakers:Elizabeth Baldwin, Ken Binmore, Peter Cramton, Michal Feldman, Paul Goldberg, Paul Klemperer, Troels Bjerre Lund, Benny Moldovanu, Tim Roughgarden, Rahul Savani, Robert Wilson. 
Participants will need to register, with a nonrefundable fee of GBP 20 which includes coffee/tea, drinks, and on Thursday a sandwich lunch at LSE. To purchase the conference ticket, please click here.
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All queries should be sent to Enfale Farooq.
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Click on a speaker name for title, abstract, and talk presentation (if available).
Wednesday 11 July 2018 
Thursday 12 July 2018 
9:30  10:15


10:00  10:10

10:15  10:40 
10:10  10:55

10:40  11:25

11:00  11:45

11:30  12:30

11:45  15:45 (reception and lunch for Prof Robert Wilson from LSE Director, with subsequent Honorary Degree ceremony as part of LSE graduation ceremony, not for Symposium participants) 
12:30  14:00 
14:00  14:45


14:50  15:35


15:35  16:00 

15:50  16:35

16:00  16:45

16:45  17:30

16:50  17:35

17:35  18:50 
17:35 
19:00 
Speaker 
Title, Links 
Abstract 
Elizabeth Baldwin 
Understanding Preferences: "Demand Types", and the Existence of Equilibrium with Indivisibilities 
An equivalence theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into "Demand Types" incorporates existing definitions (substitutes, complements, "strong substitutes", etc.) and permits new ones. Our Unimodularity Theorem generalises previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a "demand type". Contrary to popular belief, equilibrium is guaranteed for more classes of purelycomplements, than of purelysubstitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalitionformation, and the "ProductMix Auction" introduced by the Bank of England in response to the financial crisis. Joint work with Paul Klemperer. 
Ken Binmore 
On the Foundations of Decision Theory 
Bayesian decision theory was invented by Leonard Savage, who is on record as saying that it would be "preposterous" and "utterly ridiculous" to apply his theory except in a small world. But modern Bayesians proceed as though Savage's theory is always the rational way to make choices in all circumstances. What is a small world? Why did Savage restrict his theory to small worlds? Where did Savage think priors come from? What are the implications for behavioral applications? How could Savage's theory be generalized to apply to at least some large worlds? This paper offers some partial answers to such questions. 
Peter Cramton 
Market Design Inspired by Robert Wilson 
Market design combines auction and matching theory with behavioral and experimental economics to design innovative markets to better meet goals. Applications are seen in almost all markets and government programs that assign and sometimes price scarce resources. Market design research leads to a better understanding of the incentives that guide behavior. Applications include matching students to schools, interns to hospitals, and kidneys to patients. In settings where prices are used to motivate behavior, auction markets are developed to assign and price scarce resources. Applications include markets in mobile communications, electricity, financial securities, transportation, and emissions. 
Michal Feldman 
Interdependent Values Without Single Crossing 
We consider a setting where an auctioneer sells a single item to n potential agents with interdependent values. This captures settings such as valuations for artwork, oil drilling rights, broadcast rights, and many more. In the interdependent value setting, all previous work has assumed a socalled singlecrossing condition. Singlecrossing means that the impact of agent i’s private signal, s_{i}, on her own valuation is greater than the impact of s_{i} on the valuation of any other agent. It is known that without the singlecrossing condition an efficient outcome cannot be obtained. Motivated by this, we study welfare maximization for interdependent valuations through the lens of approximation. We show that, in general, without the singlecrossing condition, one cannot hope to approximate the optimal social welfare any better than the approximation given by assigning the item to a random bidder. Consequently, we introduce two valuation properties that enable positive results. The first is a relaxed, parameterized version of singlecrossing; the second is a (parameterized) submodularity condition over the signals. We obtain a host of approximation guarantees under these two notions. Joint work with Alon Eden, Amos Fiat, and Kira Goldner. 
Paul Goldberg 
The Computational Complexity of ConsensusHalving, NecklaceSplitting, and Ham Sandwich Bisection 
We present three problems that have a common theme of fair division. We present recent results showing that they are all PPAcomplete (in the talk, I will explain the complexity class PPA). These are the first examples of "natural" computational problems that are known to be PPAcomplete, where by "natural" we mean that the problem does not have a general boolean circuit (or equivalently, a polynomialtime Turing machine) embedded explicitly in the problem definition. Joint work with Aris FilosRatsikas. 
Paul Klemperer 
Wilson, Equilibrium, and Auctions 
Starting from Bob Wilson's work, I'll talk about my and coauthors' work developing practical multiproduct auctions and about choices made in developing and analysing them. My recent work on this topic is joint with Elizabeth Baldwin; some of it is joint with Paul Goldberg; all of it is influenced, of course, by Bob Wilson. 
Troels Bjerre Lund 
The Proper Way to Compute Proper Equilibria 
We provide the first pivotingtype algorithm that finds an exact proper equilibrium of a bimatrix game. This is achieved by using Lemke's algorithm to solve a linear complementarity problem (LCP) of polynomial size. This resolves an open problem in the positive: computing a proper equilibrium of a bimatrix game is in PPAD. The algorithm also computes a witness in the form of a parameterized strategy that is an εproper equilibrium for any given sufficiently small ε, allowing polynomialtime verification of the properties of the refined equilibrium. The same technique can be applied to matrix games, thereby computing a parameterized εproper strategy in polynomial time using linear programming. 
Benny Moldovanu 
A Theory of Auctions With Endogenous Valuations 
We study the revenue maximizing allocation of m units
among n symmetric agents that have unit demand and convex
preferences over the probability of receiving an object.
Such preferences are naturally induced by a game where the
agents take costly actions that affect their values before
participating in the mechanism.
Joint work with Alex Gershkov and Philipp Strack. 
Tim Roughgarden 
When Are Equilibria of Simple Auctions NearOptimal? 
This survey outlines a general and modular theory for
proving approximation guarantees for equilibria of auctions
in complex settings. This theory complements traditional
economic techniques, which generally focus on exact and
optimal solutions and are accordingly limited to relatively
stylized settings.
Joint work with Vasilis Syrgkanis and Éva Tardos. 
Rahul Savani 
End of Potential Line 
The complexity class PPAD has successfully characterized the complexity of many fixed point problems such as computing a mixed Nash equilibrium of a bimatrix game and computing a market equilibrium. The complexity class PLS has successfully characterized the complexity of computing local optima, such as a pure equilibrium in a congestion game. In this talk we introduce a complexity class, called EOPL, that lies within both PPAD and PLS. EOPL is based on the problem EndofPotentialLine, which combines the canonical problems that define PPAD and PLS. We show that finding a solution to a Pmatrix Linear Complementarity Problem (PLCP) and finding a fixed point of a piecewise linear contraction map are in this new class EOPL. In doing so, we show that solving a `Simple Stochastic Game' is in EOPL. Along the way, we get new algorithms with improved running times for both solving PLCPs and finding fixed points of contraction maps. Finally, we show that the problem of finding the sink of a Unique Sink Orientation of a cube is in EOPL; until now, this problem was not known to be in either PPAD or PLS. Joint work with John Fearnley, Spencer Gordon, and Ruta Mehta. 
Robert Wilson 
Repeated Games Played With Adaptive Automata 
We study repeated games with players' strategies restricted to be implementable by finite adaptive automata. We have some results for the prisoner's dilemma with players moving alternately. Most remarkable is an antifolk theorem: for generic stagegame payoffs there is a unique subgame perfect payoff. Moreover, for the class of boundedrecall adaptive automata with players' recalls less than 5 we find numerically that the payoff is the perfectly cooperative payoff (and conjecture that this is true generally). In my talk I will connect these results to issues in dynamic games and evolutionary processes. Joint work with Hari Govindan. 