Specker Challenge Game: Mechanism Design for Algorithm Innovation and Evaluation

How can we drive innovation towards better algorithms for NP optimization problems? NPO is the class of all NP optimization problems. The ingredients to an optimization problem are the set of input instances or problems, the set of feasible solutions, and the measure defined for a feasible solution. In a nutshell, NPO problems are optimization problems whose feasible solutions are short and easy to recognize. We design an artificial scientific community that through a game improves its knowledge. The artificial scientists question each other's beliefs. The beliefs that are successfully supported by their creators and never discounted add useful knowledge that is based on superior algorithms. The game is designed in such a way that the winning agents (= artificial scientists) have the best approximation algorithms for the NPO problems under discussion. We are in the business of designing mechanisms for a new class of NPO-based agent games that advance our understanding of NPO problems. The agents are developed by humans and the agents must survive in weekly competitions against other agents. We want to prove formal properties of the agent games to show that our mechanisms achieve what we claim: (1) a high reputation of an agent implies that the agent has strong algorithmic capabilities and vice-versa (2) algorithmic progress means that undiscounted beliefs with a high confidence are discounted. (2) means that disruptive algorithmic techniques have been brought into the game, such as SemiDefinite Programming for MAX-CSP. The agents have the flavor of a scientific community that generates many beliefs with varying confidence levels. As the game proceeds, many of the beliefs are constructively discounted while other beliefs survive all attacks, raising their confidence. As the game proceeds, some of the beliefs turn into theorems, namely when their true confidence is one. The game offers a new way to evaluate algorithms without resorting to an asymptotic analysis. The problems allowed to appear in the game are all bounded by a large constant. The starting point is an NPO problem domain that we divide into a large number of possible niches. The game is about formulating beliefs related to which niches are efficiently solvable with a certain quality. The humans produce agents that compete with each other for correctly expressing their confidence in their beliefs. As the game progresses, the agents state beliefs with higher confidence. When the confidence is 1, the beliefs are theorems. Important concepts of the …