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Operating expenses (Tables) | 12 Months Ended
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Dec. 31, 2021
Operating expenses |
Schedule of Direct Operating Expenses | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Year ended December 31, |  | ​ | 2021 |  | 2020 |  | 2019
Ancillary and logistical service expenses | ​ | ​ | $ | 52,301 | ​ | $ | 59,982 | ​ | $ | 59,252
Employee compensation expenses | ​ | ​ |  | 50,412 | ​ |  | 47,745 | ​ |  | 50,093
Buildings, facilities and technology expenses | ​ | ​ |  | 10,187 | ​ |  | 9,886 | ​ |  | 7,865
Travel, advertising and promotion expenses | ​ | ​ |  | 18,536 | ​ |  | 22,636 | ​ |  | 31,652
Other costs of services | ​ | ​ |  | 15,426 | ​ |  | 17,047 | ​ |  | 16,115
​ | ​ | ​ | $ | 146,862 | ​ | $ | 157,296 | ​ | $ | 164,977
Schedule of Selling, General and Administrative Expenses | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Year ended December 31, |  | ​ | 2021 |  | 2020 |  | 2019
Wages, salaries and benefits | ​ | ​ | $ | 293,931 | ​ | $ | 265,029 | ​ | $ | 229,624
Share-based compensation expense | ​ | ​ | ​ | 23,106 | ​ | ​ | 21,879 | ​ | ​ | 16,404
Buildings, facilities and technology expenses | ​ | ​ |  | 73,490 | ​ |  | 62,755 | ​ |  | 61,177
Travel, advertising and promotion expenses | ​ | ​ |  | 25,940 | ​ |  | 25,780 | ​ |  | 38,248
Professional fees | ​ | ​ |  | 25,969 | ​ |  | 18,220 | ​ |  | 15,572
Other SG&A expenses | ​ | ​ |  | 22,163 | ​ |  | 23,860 | ​ |  | 21,364
​ | ​ | ​ | $ | 464,599 | ​ | $ | 417,523 | ​ | $ | 382,389
Schedule Of Acquisition Related Expenses | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Year ended December 31, | ​ | 2021 |  | 2020 |  | 2019
SmartEquip: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Share-based continuing employment costs | ​ | $ | 439 | ​ | $ | — | ​ | $ | —
Other acquisition-related costs | ​ | ​ | 4,526 | ​ | ​ | — | ​ | ​ | —
​ | ​ | ​ | 4,965 | ​ | ​ | — | ​ | ​ | —
Euro Auctions: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other acquisition-related costs | ​ | ​ | 13,596 | ​ | ​ | — | ​ | ​ | —
​ | ​ | ​ | 13,596 | ​ | ​ | — | ​ | ​ | —
Rouse: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Share-based continuing employment costs | ​ | ​ | 10,332 | ​ | ​ | 802 | ​ | ​ | —
Other acquisition-related costs | ​ | ​ | 1,304 | ​ | ​ | 5,212 | ​ | ​ | —
​ | ​ | ​ | 11,636 | ​ | ​ | 6,014 | ​ | ​ | —
IronPlanet: | ​ | ​ |  |  | ​ |  |  | ​ |
Other acquisition-related costs | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 82
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other acquisitions: | ​ |  |  | ​ |  |  | ​ |  |
Continuing employment costs | ​ |  | — | ​ |  | — | ​ |  | 128
Other acquisition-related costs | ​ |  | — | ​ |  | — | ​ |  | 567
​ | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 777
​ | ​ | $ | 30,197 | ​ | $ | 6,014 | ​ | $ | 777
Schedule of Depreciation and Amortization Expenses | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Year ended December 31, |  | ​ | 2021 |  | 2020 |  | 2019
Depreciation expense | ​ | ​ | $ | 32,401 | ​ | $ | 31,330 | ​ | $ | 29,112
Amortization expense | ​ | ​ |  | 55,488 | ​ |  | 43,591 | ​ |  | 41,389
​ | ​ | ​ | $ | 87,889 | ​ | $ | 74,921 | ​ | $ | 70,501

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