This document presents a two-dimensional approach for self-coordination of agents in minority games. The approach uses an effect function to calculate the effect of an agent's previous decisions, and agents make current decisions based on their past experiences using this effect. Agents aim to attend the bar when attendance is below a social coordination parameter threshold and not attend when above the threshold. The decision making process and examples of how it works in different scenarios are provided.

1. TWO DIMENSIONAL SELF-COORDINATION
MECHANISM OF AGENTS IN MINORITY GAMES
By:
Sanaz Hasanzadeh Fard
Supervisor:
Dr. Hadi Tabatabaee Malazi
May 2019

2. Content
2/19
𝑪𝑶𝑵𝑻𝑬𝑵𝑻
INTRODUCTION
EVALUATION
PROBLEM
DEFINITION
LITERATURE
DEVISED
APPROACH

3. MOTIVATION
3/19
SMART GRID
INTRODUCTION
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
INTRODUCTION
LITERATURE

4. MOTIVATION
4/19
INTRODUCTION
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
INTRODUCTION
LITERATURE
𝑷𝒖𝒃𝒍𝒊𝒄 𝒕𝒓𝒂𝒏𝒔𝒑𝒐𝒓𝒕𝒂𝒕𝒊𝒐𝒏

5. El Farol Bar Problem
I will stay
at home
I will attend
to bar
INTRODUCTION
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
INTRODUCTION
LITERATURE
5/19

6. Literature Review
𝑨𝒅𝒂𝒑𝒕𝒊𝒗𝒆 𝑷𝒂𝒓𝒂𝒔𝒊𝒕𝒊𝒛𝒆𝒅
− 𝐹𝑜𝑐𝑢𝑠𝑖𝑛𝑔 𝑜𝑛 𝑎𝑔𝑒𝑛𝑡 𝑠𝑡𝑎𝑟𝑣𝑎𝑡𝑖𝑜𝑛
− 𝐴𝑑𝑑𝑖𝑛𝑔 𝑏𝑒ℎ𝑎𝑣𝑖𝑜𝑠𝑖𝑡
− 𝐷𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑎𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑
𝑮𝒐𝒐𝒅 𝑺𝒐𝒄𝒊𝒆𝒕𝒚 𝑬𝒒𝒖𝒊𝒍𝒊𝒃𝒓𝒊𝒖𝒎
− 𝑇𝑜𝑝𝑜𝑙𝑜𝑔𝑖𝑐𝑎𝑙 𝑛𝑒𝑡𝑤𝑜𝑟𝑘
− 𝑆𝑜𝑐𝑖𝑎𝑙 𝑝𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒𝑠
●𝐼𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐: 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑎𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
●𝐸𝑥𝑡𝑟𝑖𝑛𝑠𝑖𝑐: 𝐼𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟𝑠
INTRODUCTION
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
INTRODUCTION
LITERATURE
Shu-Heng Chen and Umberto Gostoli. Coordination in the el farol bar problem: The role of social preferences and social networks. Journal
of Economic Interaction and Coordination, 12(1):59–93, 2017.
Fatemeh Sheikhha, Hadi Tabatabaee Malazi, and Roya Amjadifard. Adaptive parasitized el farol bar problem. In Computer Science and
Information Engineering, WRI World Cong. on, volume 7, pages 422–426. IEEE, 2009.
6/19

7. Formal Problem Definition
𝒏 𝒂𝒈𝒆𝒏𝒕𝒔 C
𝒂𝒕𝒕 ≤ 𝑪
𝒂𝒕𝒕 > 𝑪
𝒎𝒆𝒎𝒐𝒓𝒚, 𝒉
𝒅 = 𝟎
𝒓 = 𝟎
𝒅 = 𝟏
𝒓 = 𝟏
𝒅 = 𝟏
𝒓 = −𝟏
Maximum starvation length
𝒓 = 𝟎
𝒓 = 𝟏
𝒓 = 𝟎
𝒓 = 𝟏
𝒓 = 𝟏
𝒓 = 𝟎
𝒓 = 𝟏
𝒓 = 𝟎
𝒓 = 𝟏𝒓 = 𝟏
𝒔𝒖 𝒕
=
𝒊=𝟏
𝒏
𝒓𝒊
𝒕
INTRODUCTION
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
INTRODUCTION
LITERATURE
7/19

8. Devised Approach (𝑻𝒘𝒐 𝑫𝒊𝒎𝒆𝒏𝒔𝒊𝒐𝒏𝒂𝒍 𝑨𝒑𝒑𝒓𝒐𝒂𝒄𝒉)
𝑬𝒇𝒇𝒆𝒄𝒕() 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏
𝐶 𝐶 𝐶
ℎ 𝑤𝑒𝑒𝑘𝑠
𝐶 𝑎 =
ℎ × 𝐶
𝑛
𝑺𝒐𝒄𝒊𝒂𝒍 𝑪𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒊𝒐𝒏 𝑷𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION
Over-crowdedUnder-crowded Optimum
8/19

9. 𝑬𝒇𝒇𝒆𝒄𝒕 𝒕 = 𝑪 − 𝒂𝒕𝒕 𝒕
𝑬𝒇𝒇𝒆𝒄𝒕 = 𝟑 𝑬𝒇𝒇𝒆𝒄𝒕 = 𝟏 𝑬𝒇𝒇𝒆𝒄𝒕 = 𝟎 𝑬𝒇𝒇𝒆𝒄𝒕 = −𝟏 𝑬𝒇𝒇𝒆𝒄𝒕 = −𝟑
𝒂𝒕𝒕 = 𝟑, 𝑪 = 𝟔 𝒂𝒕𝒕 = 𝟓, 𝑪 = 𝟔 𝒂𝒕𝒕 = 𝟔, 𝑪 = 𝟔 𝒂𝒕𝒕 = 𝟕, 𝑪 = 𝟔 𝒂𝒕𝒕 = 𝟗. 𝑪 = 𝟔

10. Decision Making Process
𝒑𝒅𝒊
𝒕
=
𝝉=𝒕−𝒉
𝒕−𝟏
(𝑬𝒇𝒇𝒆𝒄𝒕(𝝉) × 𝒅𝒊
𝝉
)
𝒑𝒅
𝐴𝑔𝑒𝑛𝑡′
𝑠𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑠𝑖𝑡𝑢𝑎𝑡𝑖𝑜𝑛
𝑏𝑎𝑠𝑒𝑑 𝑜𝑛
𝑡ℎ𝑒 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠
𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒
(𝐸𝑓𝑓𝑒𝑐𝑡 )
< 0 → 𝑑 = 0
= 0
∃ 𝐸𝑓𝑓𝑒𝑐𝑡 ≠ 0 → 𝑑 = 0
∀ 𝐸𝑓𝑓𝑒𝑐𝑡 = 0 → 𝐶 𝑎
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 < 𝐶 𝑎 → 𝑑 = 1
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 ≥ 𝐶 𝑎 → 𝑑 = 0
> 0
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 < 𝐶 𝑎 → 𝑑 = 1
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 ≥ 𝐶 𝑎 → 𝑑 = 0
10/19

11. Negative Case
𝑎𝑡𝑡 = 8
𝐸𝑓𝑓𝑒𝑐𝑡 = −2
𝑑 = 1 𝑑 = 0
𝐸𝑓𝑓𝑒𝑐𝑡 = ?
𝑎𝑡𝑡 =? 𝑎𝑡𝑡 = 6
𝐸𝑓𝑓𝑒𝑐𝑡 = 0
𝑑 = 1
𝑎𝑡𝑡 = 9
𝐸𝑓𝑓𝑒𝑐𝑡 = −3
𝑑 = 1
𝑎𝑡𝑡 = 5
𝐸𝑓𝑓𝑒𝑐𝑡 = 1
𝑑 = 1
−2 × 1 + ?× 0 + 0 × 1 + −3 × 1 + 1 × 1 = −4 < 0
𝒑𝒅𝒊
𝒕
=
𝝉=𝒕−𝒉
𝒕−𝟏
𝑬𝒇𝒇𝒆𝒄𝒕 𝝉 × 𝒅𝒊
𝝉
< 𝟎
𝑑 = 0
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION
𝒏 = 𝟏𝟎
𝒉 = 𝟓
𝑪 = 𝟔
Agent’s memory
11/19

12. Zero Case1
𝑎𝑡𝑡 = 7
𝐸𝑓𝑓𝑒𝑐𝑡 = −1
𝑑 = 1 𝑑 = 0
𝐸𝑓𝑓𝑒𝑐𝑡 = ?
𝑎𝑡𝑡 =? 𝑎𝑡𝑡 = 3
𝐸𝑓𝑓𝑒𝑐𝑡 = 3
𝑑 = 1
𝑎𝑡𝑡 = 6
𝐸𝑓𝑓𝑒𝑐𝑡 = 0
𝑑 = 1
𝑎𝑡𝑡 = 8
𝐸𝑓𝑓𝑒𝑐𝑡 = −2
𝑑 = 1
−1 × 1 + ?× 0 + 3 × 1 + 0 × 1 + −2 × 1 = 0
𝒑𝒅𝒊
𝒕
=
𝝉=𝒕−𝒉
𝒕−𝟏
𝑬𝒇𝒇𝒆𝒄𝒕 𝝉 × 𝒅𝒊
𝝉
= 𝟎
𝑑 = 0∃ 𝐸𝑓𝑓𝑒𝑐𝑡 ≠ 0 → 𝑑 = 0
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION
Agent’s memory
𝒏 = 𝟏𝟎
𝒉 = 𝟓
𝑪 = 𝟔
12/19

13. Zero Case2
𝑎𝑡𝑡 = 6
𝐸𝑓𝑓𝑒𝑐𝑡 = 0
𝑑 = 1 𝑑 = 0
𝐸𝑓𝑓𝑒𝑐𝑡 = ?
𝑎𝑡𝑡 =? 𝑎𝑡𝑡 = 6
𝐸𝑓𝑓𝑒𝑐𝑡 = 0
𝑑 = 1
𝑎𝑡𝑡 = 6
𝐸𝑓𝑓𝑒𝑐𝑡 = 0
𝑑 = 1
𝑎𝑡𝑡 =?
𝐸𝑓𝑓𝑒𝑐𝑡 =?
𝑑 = 0
0 × 1 + ?× 0 + 0 × 1 + 0 × 1 + ?× 0 = 0
𝒑𝒅𝒊
𝒕
=
𝝉=𝒕−𝒉
𝒕−𝟏
𝑬𝒇𝒇𝒆𝒄𝒕 𝝉 × 𝒅𝒊
𝝉
= 𝟎
𝐶 𝑎 =
ℎ × 𝐶
𝑛
=
5 × 6
10
= 3∀ 𝐸𝑓𝑓𝑒𝑐𝑡 = 0 → 𝐶 𝑎
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 ≥ 𝐶 𝑎 → 𝑑 = 0
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION
𝒏 = 𝟏𝟎
𝒉 = 𝟓
𝑪 = 𝟔
Agent’s memory
13/19

14. Positive Case
𝑎𝑡𝑡 = 8
𝐸𝑓𝑓𝑒𝑐𝑡 = −2
𝑑 = 1 𝑑 = 0
𝐸𝑓𝑓𝑒𝑐𝑡 = ?
𝑎𝑡𝑡 =? 𝑎𝑡𝑡 = 6
𝐸𝑓𝑓𝑒𝑐𝑡 = 0
𝑑 = 1
𝑎𝑡𝑡 = 4
𝐸𝑓𝑓𝑒𝑐𝑡 = 2
𝑑 = 1
𝑎𝑡𝑡 = 5
𝐸𝑓𝑓𝑒𝑐𝑡 = 1
𝑑 = 1
−2 × 1 + ?× 0 + 0 × 1 + 2 × 1 + 1 × 1 = 1 > 0
𝒑𝒅𝒊
𝒕
=
𝝉=𝒕−𝒉
𝒕−𝟏
𝑬𝒇𝒇𝒆𝒄𝒕 𝝉 × 𝒅𝒊
𝝉
> 𝟎
𝐶 𝑎 =
ℎ × 𝐶
𝑛
=
5 × 6
10
= 3
Computing 𝐶 𝑎
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 ≥ 𝐶 𝑎 → 𝑑 = 0
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION
𝒏 = 𝟏𝟎
𝒉 = 𝟓
𝑪 = 𝟔
Agent’s memory
14/19

15. Simulation Environment
𝑴𝒂𝒕𝒍𝒂𝒃 𝟐𝟎𝟏𝟐𝒃
− 𝐶𝑎𝑝𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑖𝑛 𝑚𝑜𝑑𝑒𝑙𝑖𝑛𝑔 𝑡ℎ𝑒
𝑝𝑟𝑜𝑏𝑙𝑒𝑚 𝑎𝑠 𝑎 𝑠𝑒𝑡 𝑜 𝑚𝑎𝑡𝑟𝑖𝑐𝑠
− 𝑆𝑝𝑒𝑒𝑑 𝑖𝑛 𝑟𝑢𝑛𝑛𝑖𝑛𝑔 𝑡ℎ𝑜𝑢𝑠𝑎𝑛𝑑𝑠
𝑜𝑓 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠
− 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑔𝑒𝑛𝑡𝑠 𝑛 = 100
− 𝑏𝑎𝑟 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝐶 = 60
− 𝑚𝑒𝑚𝑜𝑟𝑦 𝑙𝑒𝑛𝑔𝑡ℎ ℎ = 5
𝑺𝒆𝒕𝒕𝒊𝒏𝒈
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION
15/19

16. Social Utility
16/19
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION
𝑷𝒓𝒐𝒑𝒐𝒔𝒆𝒅 𝑨𝒑𝒑𝒓𝒐𝒂𝒄𝒉
𝑨𝒅𝒂𝒑𝒕𝒊𝒗𝒆 𝑷𝒂𝒓𝒂𝒔𝒊𝒕𝒊𝒛𝒆𝒅
𝑮𝒐𝒐𝒅 𝑺𝒐𝒄𝒊𝒆𝒕𝒚 𝑬𝒒𝒖𝒊𝒍𝒊𝒃𝒓𝒊𝒖𝒎

17. The Maximum Starvation Length
17/19
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
PROBLEM
DEFINITION
DEVISED
APPROACH
EVALUATION
LITERATURE
INTRODUCTION 𝑨𝒅𝒂𝒑𝒕𝒊𝒗𝒆 𝑷𝒂𝒓𝒂𝒔𝒊𝒕𝒊𝒛𝒆𝒅 𝑷𝒓𝒐𝒑𝒐𝒔𝒆𝒅 𝑨𝒑𝒑𝒓𝒐𝒂𝒄𝒉

18. Conclusion
18/19
− 𝐹𝑎𝑠𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑔𝑒𝑛𝑐𝑒
− 𝐻𝑖𝑔ℎ 𝑡𝑜𝑡𝑎𝑙 𝑢𝑡𝑖𝑙𝑖𝑡𝑦
− 𝐹𝑎𝑖𝑟 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝑷𝒓𝒐𝒑𝒐𝒔𝒆𝒅 𝒂𝒑𝒑𝒓𝒐𝒂𝒄𝒉
𝑭𝒖𝒕𝒖𝒓𝒆 𝑾𝒐𝒓𝒌𝒔
− 𝑅𝑒𝑎𝑙 𝑤𝑜𝑟𝑙𝑑 𝑝𝑟𝑜𝑏𝑙𝑒𝑚𝑠

19. Thank You For Your Attention