1. Reverse-Engineering MAC: A non-cooperative game model
Jang-Won Lee, Ao Tang, Jianwei Huang, Mung Chiang, A. Robert Calderbank
IEEE JSAC, 2007

2. Reverse engineering
Reverse engineering is the process of discovering the technological principles of a device, object, or system through analysis of its structure, function, and operation.
In this paper, by studying the current MAC protocol, they discover that the users are actually implicitly participating a non-cooperative game, with the utility function of each selfish user - a mathematical model to study the selfish behaviors in the current MAC protocol - much insights on protocol performance

3. Reverse engineering
In protocol layers - Layer 4: TCP/AQM - Layer 3: BGP - Layer 2: MAC
MAC protocols - scheduling-based (contention free): FDMA, TDMA, CDMA - random access (contention-based): Ethernet, slotted Aloha, DCF function >> Exponential Backoff (EB) protocol

4. TCP/AQM reverse engineering
Cooperative Network Utility Maximization (NUM) - utility of each user depends on its own data rate, which can be directly controlled by user itself - feedback from network

5. EB protocol reverse engineering
The utility of each link in the EB protocol directly depends on not just its own transmission but also transmissions of other links due to collisions - cannot be controlled by the link itself
There is no explicit feedback from the network
Hence, in contrast to TCP reverse engineering, a non- cooperative game model is more appropriate for the EB protocol than a global optimization model

6. System model
EB protocol - contention-window-based protocol - persistence-probability-based protocol >> each link l has its own persistence probability pl and the maximum and minimum persistence probabilities plmax and plmin >> if transmission is successful, pl= plmax >> Otherwise, , where >> if , it is called the Binary Exponential Backoff (BEB) protocol

7. Persistence probability update
- 1a is an indicator function of event a - Tl(t) is the event that link l transmits data at time-slot t - Cl(t) is the event that there is a collision to link l’s transmission given that link l transmits data at time-slot t

8. EB-MAC game
The update algorithm for expected persistence probability

9. EB-MAC game
They reverse-engineer the update algorithm in (3) as a game, in which each link l updated its persistence probability pl, to maximize its utility Ul based on strategies of the other links
, where - E is a set of links - Al={pl| plmin≤ pl ≤ plmax} is an action set of link l - Ul is a utility function of link l

10. EB-MAC game

11. EB protocol and stochastic subgradient method

12. Best response

13. Numerical results

14. Numerical results

15. Conclusion
Reverse-engineered exponential-backoff random access protocols as a non-cooperative game model
Each link is implicitly maximizing a utility function in the form of net reward for successful transmission
Due to the lack of proper feedback mechanisms in the current EB protocols, such selfish, local actions are not aligned to maximize the network-wide total utility, nor are they guaranteed to converge, even though a Nash equilibrium for the MAC game always exists