Simulating Theoretical Models of Decision Making by Prolog and Spreadsheet

updated: 11 Jan 2022

Japanese

The potential (background motivation) of my research activity is that of explication of intelligent agent architecture (i.e., mental model ) by using economic mechanisms.

Modeling Games and Economic Behavior by PROLOG

Nash equilibrium of N-person standard form game and iterated dominance (Prolog, nash1.pl, Nov 2002/Feb 2003) (v) a generalization of fixpo.pl
Nash equilibrium, iterated dominance, Nash's countinuous map (Prolog, nash01.pl, 30 Jan 2006) (=>moved below)
Nash equilibrium of a simple 2-person standard form game with Nash's continuous map (Prolog) (v) a version in spreadsheet
Complementary pivoting: Lemke-Howson algorithm (lpolp01xy.pl, Prolog, Jul 2003) refer von Stengel(2002).
labelling system for the Lemke-Howson algorithm (pf74.pl, Prolog, 19 Dec 2005) Shapley(1974)'s geometric interpretation.
A micro economics : a general equilibrium model of small economy with 2-firms-and-2-consumers (Shoven and Whalley, 1992) and Scarf's fixed point algorithm. (Prolog 7 Jan 2004) (v) Slides (Japanese) (ppt)
Theory of cooperative games and the solutions(Prolog) (v) core, nucleolus, and shapley value.
Stable marriage and Gale-Shapley algorithm (marriage0.pl, Prolog, Jul 2004) An implementation of Gale and Shapley(1962) algorithm

filter, strong simple games ufilter.pl (Prolog. 22 Oct 2009) (Errata. topology and matroid parts of this program are incorrect or under construction. A pair of new programs written in alternative way is shown below.)

Topology: a revised version of topology. New topology2022.pl (Prolog. 11 Jan 2022)

Matroid: simulating closed set definition of matroid New matroid2022.pl (Prolog. 11 Jan 2022)

Edomonds and Fulkerson(1970)'s Blocking System block.pl (Prolog. 22 Aug 2007)
Computing Walrasian equilibrium by auction: market with indivisible goods and money (price.pl. Prolog, 30 Aug-- revised 10 Sep 2005 ) (=> mechanism design section)

imperfect information game theory and game tree

modeling reputation (Prolog, May 2003) (v) this program simulates the play under rational beliefs and strategies in accordance with the sequential equilibrium of the entry-deter game example in Kreps and Wilson (1982) without modeling the extensive form.
Perfect Bayesian Equilibrium of Two Stage Imperfect Information Game (gbayes01b, Polog, 23 Dec 2003; 21 Jun 2004) (v) Modeling for strategic hypothetical reasoning in multi-stage games with uncertain payoffs by Harsanyi-transformation. 21 Jun 2004 updated with some bugfix.
Subgame perfect equilibrium of perfect information game (Prolog, Apr 2003) (v) an extended version of nash1.pl by using tree analysis utility developed in dpfirm0. modeling behavior strategies is clumsy here.
Subgame perfect equilibrium of perfect information game (Prolog) (v)(glogic01.pl, 17 Sep 2003) another brief version of game tree modeling and backward induction.
(v)(glogic02.pl, 14 Dec 2003) improved version which is compatible with the former nash1c.pl modeling.

common knowledge and decision theoretical foundation of game theory

common knowledge puzzle: the colored hat children (Prolog, Jan 2002) v
speculative traders (Prolog, Jan 2003) (v) 'no trade result' of Milgrom and Stokey, and Geanakoplos and Sebenius.
common p-belief, belief potential, and p-dominance (Prolog, Jan -Feb 2003) (v) related to the work by Monderer and Samet(1989), Morris, Rob and Shin (1995).
Newcomb problem (Prolog) (v) rational_1 yields a backward induction solution. rational_2 does dominance. (Dec 2002)
surprise test (Prolog) (v)(Dec 2002)
Cooperative game theory and solutions: Characteristic function, Imputation, Core, Nucleolus, and Shapley value (Prolog, 8 Feb 2003) (v)
Belief and Unawarenes of decision maker: (kalp01.pl. Prolog, 12 Jan 2005 ) (v)
Beleif Revision and Ramsey Test (Minimal Change) (trivia01.pl. Prolog, A Trial Version. 1 Apr 2005 ) (v) The modeling has posed by G\"ardenfors(1986). See references in the file.
Common knowledge of rationality implies backward induction: (kglp01.pl. Prolog, 17 Feb 2005 ) (v) (input data file)
Epistemic condition of Nash equilibrium: (epcn01.pl. Prolog, 10 Mar 2005 ) (v)

Mechanism design, or implementation theory

Market with indivisiblities and co-workers effect (price01.pl. Prolog, 25 Sep 2005 ) (v) An extended version of price.pl which incorporates Ma(2001)'s modeling of utility and disutility of co-workers.
Computing Walrasian equilibrium by auction: market with indivisible goods and money (price.pl. Prolog, 30 Aug-- revised 10 Sep 2005 ) (v) This code models the English auction algorithm by Gul and Stacchetti(2000) and the related topics of the modeling for exchange market with indivisibility (, multi-item auction, or job matching).
Network mechanism design theory (Prolog) (v) (2003/7/7) Marschak and Reichelstein's price mechanisms with z(a)-coordinators
Pivotal mechanism (pivotal.pl, Prolog, Jul 2004) Vickrey-Clarke-Groves mechanism(1)
Second price auction (1) naive simulation and the winner function of a combinatorial auction. (spa.pl, Prolog, Jul 2004) Vickrey-Clarke-Groves mechanism(2)
Second price auction (2): proving implementability of second price auction. (vickrey.pl, Prolog, 11 Sep 2004)
Voting and social choice rules: simple majority vote, Borda rule, pirwise majority, and Masuzawa rule. The example is cited from the book of social choice theory by Y. Saeki(1980). (v) (Prolog, 25 Jan 2004)
A sequential voting example in Dixit and Nalebuff(1991). (v) (Prolog, 9 Jan 2006)

Analyzing majority votes and the acyclic sets with the expanded versions of automated proof of the impossibility theorems (v) (sproof_f.pl, Prolog, 20 Jun 2006) (sample run and the output) (sup_vr_7alt.txt, 20 Jun 2006)

Automated design of strategic-proof social choice function (v) (sproof.pl, Prolog, 13 Jan 2006)
Prolog code for preference generation, proving Arrow's impossibility theorem, Gibbard-Satterthwaite theorem, and Sen's possibility theorem here , 22 Dec 2006)

Simulation of Nash implementation under abstract social choice environment (2001-2002,2005)
The prolog program generates SCC (social choice correspondings) and Maskin monotonicity, Ess-monotonicity, NVP, Pareto principle and so on. (More..)

Ambiguous beliefs, Knightian uncertainty, and multipleself

belief function, DS-updating, and Choquet expected utility (Prolog) (v) Dempster-Shafer's model of uncertain or ambiguous beliefs.
Equilibrium under uncertainty (Prolog, Jan 2004) (belief02.pl, source code)
This program simulates cooperative play in 2-stage prisoners dilemma game (2ipd) analyzed in Dow and Werlang(1994).
Nash equilibrium under Uncertainty: (beleq03.pl. Prolog, 13 Mar 2004 ) equilibrium in beliefs by Dow and Werlang(1994) for N=2 and the generalized version by Eichberger and Kelsey(2000) for N>=2.
Dempster-Shafer equilibrium (and Perfect Bayes equilibrium) of signaling games: (dse0.pl. Prolog, 25 Jun 2004 ) Uncertainty averse strategic equilibria of signaling games by Eichberger and Kelsey(2000) and Ryan(2002) (v)

search models

search with reltive rank, search with bounded memory, dynamic allocation index and so on.

Optimal stopping with relative rank(Prolog, Spreadsheet) (v)
Branch and Bound: 0-1 knapsack problem (Prolog) (v) (1 Sep 2003)
EBA(eliminating by aspects) (Prolog) (v) EBA is a model of probabilistic selection from the menue of consumption goods by iterative elimination by attending thier attractive aspects (Tversky, 1972).
DAI(Gittins-Jones Dynamic Allocation Index ) (Prolog, 11 Aug 2004) (Under Construction) (v) This program intended to reproduce the algorithm in Gittins(1979) and the numerical results in the companion paper (Gittins and Jones, 1974).
This program has tested, with a lower approximation level, A+B=<9, comparing with the experimental data in Gittins and Jones(1979). Tentative results (21-A-B<=6) are downloadable. (data in spreadsheet) (data in text file written in loadable prolog code.)
Optimal design for managerial hierarchies (Prolog) (v) (2003/3/25) Generating and evaluate trees with cost function of node capacities and revenue function which is increasing in the number of levels. This program has inspired by Prat(1997), and also Radner(1993).

Library for Prolog

set operations (set.pl)
(2)arithmetic (math1.pl)
(3)Japanese characters (moji.pl)
(4)input/output (menu.pl)

Spreadsheet Modeling for Games and Economic Behavior

Nash(1951)'s continuous map for 2-person 2x2 bimatrix games : a figure (Spreadsheet) (xls file). A limit-cycle, or a fixed point which is not stable. (figure, jpg)
Cournot's duopoly (Spreadsheet, cournot13.xls , May 2013)
chaotic patterns in Cournot oligopoly (Spreadsheet, 28--29 Dec 2003) (zip file) I tried to reproduce a dynamic game of Cournot oligopoly with 3 competitors by Agiza(1998) who modified Puu's model. (figure1, jpg) (figure2, jpg)
Beer Game: A Supply Chain Simulation beer.xls (Spreadsheet, 2 Nov 2003) Beer Game simulates unexpected inventory phenomena in real business supply chain.
a simple agency problem: Principal-Agent relationship and moral hazard (agency.xls) (Spreadsheet, 10 Nov 2007)
optimal contract and renegotiation: analyzing the hold-up problem (contract.xls) (Spreadsheet, 29 Nov 2007) (Japanese)
Voluntary disclosure (disclose.xls. Spreadsheet, Nov 2004 )
A game theoretical application of accounting. Verifiability of evidences and the worst case reasoning make the informant to disclose his/her private information rationally.
duoploy market models: Cournot, Stackelberg, Bertrand, and Hotelling (Spreadsheet, Dec 2003/ 6,11,15 Dec 2005) (xls file) Quantity-based imperfect competitive equilibrium by Cournot or Stackelberg. Price-based competition by Bertrand or Hotelling.
chaos: Gumowski-Mira map (Spreadsheet, 17 Sep 2003) (xls file) (zip file) Classical patterns of discrete chaotic dynamics. Fingers-like attractor (figure, jpg)

AHP analysis of cognitive skewness in music tuning systems tone_ahp_e.xls (Spreadsheet, 9 Feb 2008; revised 16 Feb 2008)
Optimal design for managerial hierarchies (Spreadsheet) (xls file) (2003/10/02) A DP model of optimal managerial hierarchy with recursive production technology and incentive scheme by Qian(1994).
Incentive control (Nash implementation) (Spreadsheet) (xls file) (1998/2002)
2x2 bimatrix game analyzer: Nash mapping, fictitious play(Brown-Robinson's mapping), pivot procedure, and EWA. an extended version of above. (Spreadsheet fixpo04a.xls, 24 Jul-19 Aug 2004) (zip 444KB) a developmental version of generalized learning process (F.P.) by Miyasawa(1961). (Spreadsheet fixpo04c.xls, 23 Sep 2004) (zip 444KB)
Shapley-Shubik power index for the weighted majority vote (ss_index09.xls) (Spreadsheet, 29 Nov 2007; revised 28 Nov 2009)
A visualization: expected utility and alternative models with decision weights (Spreadsheet) (xls file) (2001)
Elicitation of decision weights --- trade-off method (Spreadsheet)(xls file) (2001)
A multipleself: Hyperbolic discounting (Spreadsheet)(xls file) (2001)
Updating ambigous beliefs (Spreadsheet)(xls file) (2001)
A simulation of DAI (spreadsheet)(xls file) (incomplete)

articles

social choice logic programming and Arrow's theorem
(more...)
Decisiveness of Decision Maker: A Multiple-Self Method(2001)
(working paper)(pdf zipped 350KB)
Modeling game theory under Uncertainty: A modelbase system. (pdf) reported in the spring meeting of JASMIN 2004.
Modeling cognitive processes of a decision maker. (pdf) An essay based on my presentation in LGS6 2009.
A preference aggregation based cognitive modeling: the discursive dilemma solves the Wason selection task (presentation at Jasmin06 autumn meeting: jasmin06at-presen.pdf, 27 Dec 2006 Japanese)
Preference Aggregation Based Cognitive Modeling: An Alternative Explanation of the Wason Selection Task. working paper (1 Feb 2008)

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