Liquidity Game - IJCAI 2024 Supplementary

Thank you for taking the time to refer to this document. For ease of reference, a short table of contents is below. This document contains proofs, code notes, derivations and details regarding data used in, and supplementary to, the submission entitled ”Non cooperative Liquidity Games and their application to bond market trading”. All python code can be found in the zip file and referenced below.

1 Code: Empirical Computational Game theory code

In support of proofs and validation of the associated submission the following is a set of attached files with descriptions:

1.1 Nash and mixed Nash computational analysis

File: IJCAI Mixed Nash 2 player.py

1.2 Bayesian Nash Simulation and Analysis

See python code File: Bayesian Nash simulation.py - this file contains the simulator of the main game with a range of values for each player. File: ”Analysis Bayesian Nash simulation.py” provides analysis code and output is demonstrated in file ”example BN output.txt”. Also, a sample of a Bayesian setting with 10,000 simulations and initial $B_{i} \in 1 \ldot 1000 a n d B_{j} \in - 1000 \ldot - 1 c a n b e f o u n d i n f i l e ”Sample Bayesian simulation 10k.xlsx” . 2section 22§22DerivationofNEforBi=2andBj=-2 T h i s d e r i v a t i o n r e l a t e s t o d e t a i l s i n 4.1: Perfect information games o f t h e m a i n p a p e r (s e c t i o n b e g i n n i n g l i n e 362 a n d f o l l o w i n g) . Trivialexample:MixedStrategyEquilibri$