Quartz 4

Higher-order game theory

2 min read

Abstract

My collaboration with Martín Escardó on Higher-Order Game Theory began in 2007 (when we met in conferences in Brazil and Poland), with our first paper [1] published in 2010. At the time, I was studying bar-recursive interpretations of analysis, while Martín was developing selection functions as a computational interpretation of the topological notion of compactness. We soon observed that the construction underlying Tychonoff’s theorem (the product of selection functions) was very similar to Spector’s bar recursion. This insight led us to generalise the theory of selection functions and discover a new connection to the backward induction principle in game theory, used to compute sub-game perfect equilibria. In the years that followed, we continued to collaborate, now with a dozen papers exploring new applications of this theory to proof theory, game theory, and topology. In this talk, I will survey our main results and present an overview of our ongoing work in this area.

[1] Martín Escardó and Paulo Oliva, Selection functions, bar recursion and backward induction, Mathematical Structures in Computer Science, 20(2):127-168, 2010

Talk Details

Speaker: Paulo Oliva (Queen Mary University of London, UK)
Event: Types and Topology Workshop in Honour of Martin Escardo’s 60th Birthday
Date: Wednesday 17 December 2025
Time: 15:05
Slides: Available

Key Topics

  • Higher-order game theory
  • Selection functions
  • Bar recursion
  • Backward induction
  • Tychonoff’s theorem
  • Spector’s bar recursion
  • Sub-game perfect equilibria
  • Compactness
  • Proof theory

Collaboration History

The collaboration between Oliva and Escardó began in 2007 at conferences in Brazil and Poland, leading to over a dozen joint papers spanning proof theory, game theory, and topology. This represents one of Escardó’s most productive long-term collaborations.

Graph View

Backlinks